SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  Schedule 13D

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 20)*

                               TREMONT CORPORATION
                                (Name of Issuer)

                          Common Stock, $1.00 par value
                         (Title of Class of Securities)

                                   894745 20 7
                                 (CUSIP Number)

                                STEVEN L. WATSON
                              THREE LINCOLN CENTRE
                                   SUITE 1700
                                5430 LBJ FREEWAY
                            DALLAS, TEXAS 75240-2694
                                 (972) 233-1700
                  (Name, Address and Telephone Number of Person
                Authorized to Receive Notices and Communications)

                                  July 26, 2002
                      (Date of Event which requires Filing
                               of this Statement)

         If the filing person has  previously  filed a statement on Schedule 13G
to report the  acquisition  that is the  subject of this  Schedule  13D,  and is
filing  this  schedule  because  of  sections   240.13d-1(e),   240.13d-1(f)  or
240.13d-1(g), check the following box. [ ]

         *The  remainder  of this cover page shall be filled out for a reporting
person's  initial  filing on this  form with  respect  to the  subject  class of
securities,  and for any subsequent amendment containing information which would
alter disclosures provided in a prior cover page.

         The information  required on the remainder of this cover page shall not
be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise  subject to the  liabilities of that section of
the Act but shall be subject to all other  provisions of the Act  (however,  see
the Notes).

                         (Continued on following pages)






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Tremont Group, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      OO

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,141,421
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,141,421

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,141,421

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.0%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO







CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Tremont Holdings, LLC

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,149,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,149,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,149,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      OO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      NL Industries, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      New Jersey

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,149,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,149,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,149,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Valhi, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC and BK

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Valhi Group, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Nevada

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      National City Lines, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      NOA, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Texas

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Dixie Holding Company

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Dixie Rice Agricultural Corporation, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Louisiana

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Southwest Louisiana Land Company, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Louisiana

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Contran Corporation

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Delaware

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Harold Simmons Foundation, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [   ]

             (b)  [   ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Texas

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      The Combined Master Retirement Trust

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [   ]

             (b)  [   ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Texas

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      EP






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Harold C. Simmons

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP(SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      USA

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      -0-

    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [ X ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      0.0%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      IN






                                AMENDMENT NO. 20
                                 TO SCHEDULE 13D

         This amended  statement on Schedule 13D (this  "Statement")  relates to
the  common  stock,  par value  $1.00  per  share  (the  "Shares"),  of  Tremont
Corporation,  a Delaware corporation (the "Company").  Items 2, 3, 4, 5, 6 and 7
of this Statement are hereby amended as set forth below.

Item 2.  Identity and Background.

         Item 2 is amended as follows.

         (a) This Statement is filed (i) by Tremont Group, Inc. ("TGI"), Tremont
Holdings,  LLC ("TRE Holdings") and Valhi, Inc.  ("Valhi") as the direct holders
of Shares,  (ii) by virtue of the direct and indirect ownership of securities of
TGI, by TRE Holdings and Valhi, NL Industries,  Inc. ("NL"),  Valhi Group,  Inc.
("VGI"),  National  City Lines,  Inc.  ("National"),  NOA, Inc.  ("NOA"),  Dixie
Holding Company ("Dixie  Holding"),  Dixie Rice Agricultural  Corporation,  Inc.
("Dixie Rice"),  Southwest Louisiana Land Company, Inc.  ("Southwest"),  Contran
Corporation ("Contran"),  the Harold Simmons Foundation, Inc. (the "Foundation")
and the Combined Master Retirement Trust (the "CMRT") and (iii) by virtue of his
positions  with Contran and certain of the other  entities (as described in this
Statement),  by Harold C. Simmons  (collectively,  the "Reporting Persons").  By
signing this  Statement,  each  Reporting  Person agrees that this  Statement is
filed on its or his behalf.

         TGI,  TRE Holdings  and Valhi are the direct  holders of  approximately
80.0%, 0.1% and 0.1%,  respectively,  of the 6,424,858 Shares  outstanding as of
May 13, 2002  according to the Company's  Quarterly  Report on Form 10-Q for the
quarter  ended March 31, 2002 (the  "Outstanding  Shares").  Together,  TGI, TRE
Holdings and Valhi may be deemed to control the Company.  Valhi and TRE Holdings
are the  direct  holders  of 80.0% and 20.0%,  respectively  of the  outstanding
common  stock of TGI.  Together  Valhi and TRE Holdings may be deemed to control
TGI.  NL is the sole  member of TRE  Holdings  and may be deemed to control  TRE
Holdings.  Valhi and the Company are the direct holders of  approximately  61.8%
and 21.0%, respectively,  of the outstanding common stock of NL and together may
be deemed to control NL. VGI,  National,  Contran,  the Foundation,  the Contran
Deferred Compensation Trust No. 2 (the "CDCT No. 2") and the CMRT are the direct
holders of 80.6%, 9.5%, 2.1%, 1.4%, 0.4% and 0.1%,  respectively,  of the common
stock of Valhi.  Together,  VGI,  National  and Contran may be deemed to control
Valhi.  National,  NOA and Dixie Holding are the direct holders of approximately
73.3%,  11.4% and 15.3%,  respectively,  of the outstanding common stock of VGI.
Together,  National, NOA and Dixie Holding may be deemed to control VGI. Contran
and NOA are the direct holders of approximately  85.7% and 14.3%,  respectively,
of the  outstanding  common  stock of  National  and  together  may be deemed to
control National.  Contran and Southwest are the direct holders of approximately
49.9%  and  50.1%,  respectively,  of the  outstanding  common  stock of NOA and
together may be deemed to control NOA.  Dixie Rice is the direct  holder of 100%
of the  outstanding  common stock of Dixie  Holding and may be deemed to control
Dixie Holding.  Contran is the holder of 100% of the outstanding common stock of
Dixie Rice and may be deemed to  control  Dixie  Rice.  Contran is the holder of
approximately  88.9% of the  outstanding  common stock of  Southwest  and may be
deemed to control Southwest.

         Substantially  all of  Contran's  outstanding  voting  stock is held by
trusts  established  for the benefit of certain  children and  grandchildren  of
Harold C. Simmons (the "Trusts"),  of which Mr. Simmons is the sole trustee.  As
sole trustee of each of the Trusts, Mr. Simmons has the power to vote and direct
the  disposition of the shares of Contran stock held by each of the Trusts.  Mr.
Simmons, however,  disclaims beneficial ownership of any shares of Contran stock
that the Trusts hold.

         The Foundation  directly holds  approximately  1.4% of the  outstanding
Valhi common  stock.  The  Foundation is a tax-exempt  foundation  organized for
charitable  purposes.  Harold C.  Simmons is the chairman of the board and chief
executive officer of the Foundation and may be deemed to control the Foundation.

         The CDCT No. 2 directly  holds  approximately  0.4% of the  outstanding
Valhi common stock. U.S. Bank National  Association serves as the trustee of the
CDCT No. 2. Contran  established the CDCT No. 2 as an irrevocable  "rabbi trust"
to assist Contran in meeting certain deferred  compensation  obligations that it
owed to Harold C. Simmons.  If the CDCT No. 2 assets are insufficient to satisfy
such  obligations,   Contran  is  obligated  to  satisfy  the  balance  of  such
obligations  as they come due.  Pursuant to the terms of the CDCT No. 2, Contran
(i) retains the power to vote the shares of Valhi common stock held  directly by
the CDCT No. 2, (ii) retains dispositive power over such shares and (iii) may be
deemed the indirect beneficial owner of such shares.

         The CMRT directly holds approximately 0.1% of the outstanding shares of
Valhi  common  stock.  Valhi  established  the  CMRT as a trust  to  permit  the
collective  investment  by master  trusts  that  maintain  the assets of certain
employee  benefit plans Valhi and related  companies  adopt.  Mr. Simmons is the
sole trustee of the CMRT and a member of the trust investment  committee for the
CMRT. Mr. Simmons is a participant in one or more of the employee  benefit plans
that invest through the CMRT.

         Valmont Insurance  Company  ("Valmont") and a subsidiary of NL directly
own 1,000,000 shares and 1,186,200 shares, respectively,  of Valhi common stock.
Valhi is the direct  holder of 100% of the  outstanding  common stock of Valmont
and may be deemed to control Valmont. Pursuant to Delaware law, Valhi treats the
shares of Valhi  common  stock  that  Valmont  and the  subsidiary  of NL own as
treasury  stock for voting  purposes and for the purposes of this  Statement are
not deemed outstanding.

         Mr.  Harold C.  Simmons is  chairman  of the board and chief  executive
officer of TGI, Valhi, VGI, National,  NOA, Dixie Holding, Dixie Rice, Southwest
and Contran.  Mr.  Simmons is also chairman of the board of NL and a director of
the Company.

         By virtue of the holding of the offices,  the stock  ownership  and his
service as trustee,  all as described  above,  (a) Mr.  Simmons may be deemed to
control the  entities  described  above and (b) Mr.  Simmons and certain of such
entities  may be deemed  to  possess  indirect  beneficial  ownership  of Shares
directly held by certain of such other entities.  However, Mr. Simmons disclaims
beneficial  ownership of the Shares beneficially owned,  directly or indirectly,
by any of such entities.

         Harold C.  Simmons'  spouse is the  direct  owner  69,475  shares of NL
common stock. Mr. Simmons may be deemed to share indirect  beneficial  ownership
of such shares. Mr. Simmons disclaims all such beneficial ownership.

         Certain information  concerning the directors and executive officers of
the Reporting  Persons,  including offices held by Mr. Simmons,  is set forth on
Schedule B attached hereto and incorporated herein by reference.

         (d) None of the  Reporting  Persons or, to the best  knowledge  of such
persons,  any of the  persons  named in  Schedule B to this  Statement  has been
convicted in a criminal  proceeding  in the past five years  (excluding  traffic
violations or similar misdemeanors).

         (e) None of the  Reporting  Persons or, to the best  knowledge  of such
persons,  any person  named in  Schedule B to this  Statement,  was a party to a
civil proceeding of a judicial or administrative body of competent  jurisdiction
as a result of which such  person was or is  subject  to a  judgment,  decree or
final  order  enjoining  future  violations  of,  or  prohibiting  or  mandating
activities subject to, federal or state securities laws or finding any violation
with respect to such laws.

         (f) Harold C.  Simmons and all the persons  named on Schedule B to this
Statement are citizens of the United  States,  except as otherwise  indicated on
such Schedule.

Item 3.  Source and Amount of Funds or Other Consideration.

         Item 3 is amended as follows.

         The Reporting Persons understand that the funds required by the persons
named in  Schedule B to this  Statement  to acquire  Shares  (other  than Shares
Harold C.  Simmons may be deemed to own  beneficially)  were from such  person's
personal funds.

Item 4.  Purpose of Transaction.

         No change to Item 4 except for the following:

         On July 26, 2002,  Valhi sent a letter to the board of directors of the
Company proposing (the "Proposal") a merger of Valhi and the Company pursuant to
which stockholders of the Company, other than Valhi, would receive between 2 and
2.5  shares of  Valhi's  common  stock,  par value  $0.01  per  share,  for each
outstanding Share held. A copy of the letter is attached hereto as Exhibit 8 and
incorporated  herein by reference  (the  "Proposal  Letter").  On July 26, 2002,
Valhi  issued a press  release  announcing  the  Proposal.  A copy of the  press
release is attached hereto as Exhibit 9 and incorporated herein by reference. On
July 29, 2002, the Company issued a press release  announcing its receipt of the
Proposal  Letter and that the Company  expects its board of  directors to form a
special  committee  comprised of board members  unrelated to Valhi to review the
Proposal.  A copy of the press  release  is  attached  hereto as  Exhibit 10 and
incorporated  herein by reference.  There is no assurance  that any  transaction
will be consummated under the terms of the Proposal or otherwise.

         Beginning on July 29, 2002, several purported  stockholder class action
lawsuits were filed against the Company and Valhi and the Company's directors on
behalf of the Company's  stockholders  other than Valhi and its affiliates.  The
complaints  allege,  among  other  things,  that the  defendants  have  breached
fiduciary  duties owed to the  Company's  stockholders  other than Valhi and its
affiliates  with respect to the  Proposal.  Each of the  complaints  seeks class
certification  and to  enjoin  the  consummation  of the  Proposal  and  recover
attorneys'  fees and expenses.  The complaints  also seek an award of damages if
the Proposal is  consummated.  None of the  defendants  has yet responded to the
lawsuits.

         Depending  upon  their   evaluation  of  the  Company's   business  and
prospects,  and  upon  future  developments  (including,  but  not  limited  to,
performance of the Shares in the market, availability of funds, alternative uses
of funds, the Reporting Persons' tax planning objectives and money, stock market
and general economic conditions), any of the Reporting Persons or other entities
or persons  that may be deemed to be  affiliated  with  Contran may from time to
time  purchase  Shares,  and any of the Reporting  Persons or other  entities or
persons that may be deemed to be  affiliated  with Contran may from time to time
dispose  of all or a portion  of the Shares  held by such  entity or person,  or
cease buying or selling Shares.  Any such  additional  purchases or sales of the
Shares may be in open market or privately negotiated transactions or otherwise.

         As described under Item 2, Harold C. Simmons,  through Contran,  may be
deemed to control the Company.

         The  information  included in Item 6 of this Statement is  incorporated
herein by reference.

         The Reporting Persons understand that prior purchases of Shares by each
of the  persons  named in  Schedule B to this  Statement  (other  than Harold C.
Simmons) were made for the purpose of each such person's personal investment.

         Certain of the persons named in Schedule B to this Statement, namely J.
Landis  Martin,  Harold C.  Simmons,  Glenn R.  Simmons,  Thomas P. Stafford and
Steven L.  Watson,  are  directors  or  officers  of the Company and may acquire
Shares from time to time pursuant to benefit plans that the Company  sponsors or
other compensation arrangements with the Company.

         Except as described in this Item 4, none of the Reporting  Persons nor,
to the best  knowledge of such persons,  any other person named in Schedule B to
the this Statement has formulated any plans or proposals that relate to or would
result in any matter  required to be  disclosed  in response to  paragraphs  (a)
through (j) of Item 4 of Schedule 13D.

Item 5.  Interest in Securities of the Issuer.

         Item 5 is amended as follows.

         (a) TGI, TRE Holdings and Valhi are the direct  holders of 5,141,421 of
the Shares (approximately 80.0% of the Outstanding Shares),  8,167 of the Shares
(approximately  0.1%  of  the  Outstanding  Shares)  and  5,000  of  the  Shares
(approximately 0.1% of the Outstanding Shares), respectively.

         By virtue of the relationships described under Item 2 of this
Statement:

                  (1)  TRE  Holdings  and  NL  may  each  be  deemed  to be  the
         beneficial  owner of the 5,149,588 Shares  (approximately  80.2% of the
         Outstanding Shares) that TGI and TRE Holdings directly hold; and

                  (2) Valhi,  VGI,  National,  NOA, Dixie  Holding,  Dixie Rice,
         Southwest,  Contran, the Foundation, the CMRT and Harold C. Simmons may
         each be  deemed  to be the  beneficial  owner of the  5,154,588  Shares
         (approximately  80.2% of the Outstanding Shares) that TGI, TRE Holdings
         and Valhi directly hold.

         Mr. Simmons disclaims beneficial ownership of all Shares.

         The Reporting Persons  understand,  based on ownership filings with the
Securities  and  Exchange  Commission  (the  "Commission")  or upon  information
provided  by the  persons  listed on  Schedule  B to this  Statement,  that such
persons may be deemed to own  beneficially the Shares as indicated on Schedule C
to this Statement.

         (b)      By virtue of the relationships described in Item 2:

                  (1) TGI may be deemed  to share  the power to vote and  direct
         the disposition of the Shares that TGI directly holds;

                  (2) TRE  Holdings and NL may each be deemed to share the power
         to vote and  direct  the  disposition  of the  Shares  that TGI and TRE
         Holdings directly hold; and

                  (3) Valhi,  VGI,  National,  NOA, Dixie  Holding,  Dixie Rice,
         Southwest,  Contran, the Foundation, the CMRT and Harold C. Simmons may
         each be deemed to share the power to vote and direct the disposition of
         the Shares that TGI, TRE Holdings and Valhi directly hold.

         (d) Each of TGI,  TRE  Holdings  and Valhi has the right to receive and
the power to direct the receipt of dividends  from,  and proceeds  from the sale
of, the 5,141,421, 8,167 and 5,000 Shares, respectively, held by such entity.

Item 6.  Contracts, Arrangements, Understandings or Relationships With Respect
to Securities of the Issuer.

         Item 6 is amended as follows.

         The  information  included  in  Item  4 of  this  Statement  is  hereby
incorporated herein by reference.

         Except for the provisions and agreements  previously  described in this
item,  none of the Reporting  Persons or, to the best knowledge of such persons,
any person named in Schedule B to this Statement has any contract,  arrangement,
understanding or relationship  (legal or otherwise) with any person with respect
to securities of the Company,  including, but not limited to, transfer or voting
of  any  such  securities,  finder's  fees,  joint  ventures,  loans  or  option
arrangements,  puts or calls,  guarantees  of  profits,  division  of profits or
losses, or the giving or withholding of proxies.

Item 7.  Material to be Filed as Exhibits.

         Item 7 is amended and restated as follows.

Exhibit  1        Credit  Agreement  dated as of November 6, 1998 among Valhi,
                  Inc., the financial  institutions from time to time that are a
                  party thereto and Societe  Generale,  Southwest Agency, as the
                  administrative agent, issuing bank and arranger  (incorporated
                  by reference to Exhibit 1 to Amendment  No. 59 to the Schedule
                  13D  filed  on  November  23,  1999  with the  Securities  and
                  Exchange Commission by Tremont Corporation,  Valmont Insurance
                  Company,  Valhi, Inc., Valhi Group, Inc., National City Lines,
                  Inc.,   NOA,   Inc.,   Dixie  Holding   Company,   Dixie  Rice
                  Agricultural  Corporation,   Inc.,  Southwest  Louisiana  Land
                  Company,  Inc.,  Contran  Corporation,   The  Combined  Master
                  Retirement  Trust,  the Harold  Simmons  Foundation,  Inc. and
                  Harold C. Simmons with respect to the common stock,  par value
                  $0.125 per share, of NL Industries, Inc.).

Exhibit  2        First Amendment Agreement dated as of November 5, 1999 among
                  Valhi, Inc., the financial institutions from time to time that
                  are a party thereto and Societe Generale, Southwest Agency, as
                  the   administrative   agent,   issuing   bank  and   arranger
                  (incorporated by reference to Exhibit 2 to Amendment No. 60 to
                  the   Schedule  13D  filed  on  December  14,  1999  with  the
                  Securities  and Exchange  Commission  by Tremont  Corporation,
                  Valmont Insurance  Company,  Valhi,  Inc., Valhi Group,  Inc.,
                  National City Lines,  Inc., NOA, Inc.,  Dixie Holding Company,
                  Dixie Rice Agricultural Corporation, Inc., Southwest Louisiana
                  Land Company,  Inc., Contran Corporation,  The Combined Master
                  Retirement  Trust,  the Harold  Simmons  Foundation,  Inc. and
                  Harold C. Simmons with respect to the common stock,  par value
                  $0.125 per share, of NL Industries, Inc.).

Exhibit  3        Second  Amendment  Agreement  dated as of  November  3, 2000
                  among Valhi,  Inc.,  the financial  institutions  from time to
                  time  that  are  a  party   thereto  and  U.S.  Bank  National
                  Association  as the  administrative  agent,  issuing  bank and
                  arranger  (incorporated by reference to Exhibit 3 to Amendment
                  No. 15 to this Statement).

Exhibit  4        Form of  Accession  Agreement  dated as of  December 1, 2000
                  among  Valhi,   Inc.,   the  Banks  and  U.S.   Bank  National
                  Association, as the administrative agent of the banks, and the
                  related  promissory note in the original  principal  amount of
                  $5.0  million  payable  to the  order  of Texas  Capital  Bank
                  (incorporated by reference to Exhibit 4 to Amendment No. 63 to
                  the  Schedule  13D  filed  on  September  25,  2001  with  the
                  Securities  and Exchange  Commission  by Tremont  Corporation,
                  Tremont Group, Inc., Tremont Holdings, LLC, Valhi, Inc., Valhi
                  Group,  Inc.,  National City Lines,  Inc.,  NOA,  Inc.,  Dixie
                  Holding Company,  Dixie Rice Agricultural  Corporation,  Inc.,
                  Southwest Louisiana Land Company,  Inc., Contran  Corporation,
                  The  Combined  Master  Retirement  Trust,  the Harold  Simmons
                  Foundation,  Inc.  and Harold C.  Simmons  with respect to the
                  common stock,  par value $0.125 per share,  of NL  Industries,
                  Inc.).

Exhibit  5        Stock  Purchase  Agreement  dated  as of  November  7,  2000
                  between  Valhi,  Inc. and J. Landis  Martin  (incorporated  by
                  reference to Exhibit 4 to Amendment No. 16 to this Statement).

Exhibit  6        Certificate  of  Incorporation   of  Tremont  Group,   Inc.
                  (incorporated by reference to Exhibit 5 to Amendment No. 17 to
                  this Statement).

Exhibit  7        Voting  Agreement  dated as of  December  31,  2000  between
                  Valhi,  Inc.  and  Tremont  Holdings,   LLC  (incorporated  by
                  reference to Exhibit 6 to Amendment No. 17 to this Statement).

Exhibit  8        Letter dated July 26, 2002 from Valhi,  Inc. to the board of
                  directors of Tremont Corporation (incorporated by reference to
                  Exhibit 99.1 to the Current Report on Form 8-K of Valhi,  Inc.
                  the date of event of which is July 26, 2002).

Exhibit  9        Press   Release   of  Valhi  Inc.   dated  July  26,   2002
                  (incorporated  by  reference  to Exhibit  99.2 to the  Current
                  Report on Form 8-K of Valhi,  Inc.  the date of event of which
                  is July 26, 2002).

Exhibit  10*      Press Release of Tremont Corporation dated July 29, 2002.

----------

*        Filed herewith.





                                    Signature

         After reasonable  inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this Statement is true,  complete and
correct.

Date:  August 2, 2002




                                                          /s/ Harold C. Simmons
                                                          ----------------------
                                                          Harold C. Simmons
                                                          Signing in the
                                                          capacities listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                    Signature

         After reasonable  inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this Statement is true,  complete and
correct.

Date:  August 2, 2002




                                                          /s/ J. Landis Martin
                                                          ----------------------
                                                          J. Landis Martin
                                                          Signing in the
                                                          capacity listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                    Signature

         After reasonable  inquiry and to the best of my knowledge and belief, I
certify that the information  set forth in this Statement is true,  complete and
correct.

Date:  August 2, 2002





                                                          /s/ Steven L. Watson
                                                          ----------------------
                                                          Steven L. Watson
                                                          Signing in the
                                                          capacities listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                   SCHEDULE A


HAROLD C. SIMMONS, in his individual capacity and as trustee for THE COMBINED
MASTER RETIREMENT TRUST.


J. LANDIS MARTIN, as president of each of:

NL INDUSTRIES, INC.
TREMONT HOLDINGS, LLC

STEVEN L. WATSON, as president or vice president of each of:

CONTRAN CORPORATION
DIXIE HOLDING COMPANY
DIXIE RICE AGRICULTURAL CORPORATION, INC.
HAROLD SIMMONS FOUNDATION, INC.
NATIONAL CITY LINES, INC.
NOA, INC.
SOUTHWEST LOUISIANA LAND COMPANY, INC.
TREMONT GROUP, INC.
VALHI GROUP, INC.
VALHI, INC.





                                   Schedule B

         Schedule B is hereby amended and restated as follows:

         The  names  of  the  directors   and  executive   officers  of  Contran
Corporation  ("Contran"),  Dixie Holding Company ("Dixie  Holding"),  Dixie Rice
Agricultural  Corporation,  Inc. ("Dixie Rice"), the Harold Simmons  Foundation,
Inc. (the "Foundation"),  National City Lines, Inc. ("National"), NL Industries,
Inc.  ("NL"),  NOA,  Inc.  ("NOA"),   Southwest  Louisiana  Land  Company,  Inc.
("Southwest"), Tremont Group, Inc. ("TGI"), Valhi Group, Inc. ("VGI") and Valhi,
Inc.  ("Valhi"),  and their present  principal  occupations are set forth below.
Except as  otherwise  indicated,  each such  person is a citizen  of the  United
States of  America  and the  business  address  of each such  person is 5430 LBJ
Freeway, Suite 1700, Dallas, Texas 75240.



           Name                                             Present Principal Occupation
-----------------------------                             ---------------------------------
                                                       
Eugene K. Anderson                                        Vice president of Contran, Dixie Holding, Dixie Rice, National,
                                                          NOA, Southwest, TGI, VGI and Valhi; and treasurer of the
                                                          Foundation.

Thomas E. Barry (1)                                       Vice president for executive affairs at Southern  Methodist
                                                          University  and  professor of marketing in the Edwin L. Cox
                                                          School of Business at Southern Methodist University;  and a
                                                          director of Valhi.

Norman S. Edelcup (2)                                     Senior  vice  president  business  development  of  Florida
                                                          Savings  Bancorp;  director  of Valhi;  and  trustee of the
                                                          Baron Funds, a mutual fund group.

Lisa Simmons Epstein                                      Director and president of the Foundation.

David B. Garten (3)                                       Vice  president,  general  counsel and secretary of NL; and
                                                          vice  president  and  secretary  of Tremont  Holdings,  LLC
                                                          ("TRE Holdings").

Edward J. Hardin (4)                                      Partner  of the law  firm of  Rogers &  Hardin  LLP;  and a
                                                          director of Valhi.

Robert D. Hardy (3)                                       Vice  president,  chief financial  officer,  controller and
                                                          treasurer of NL and vice  president  and  controller of TRE
                                                          Holdings.

J. Mark Hollingsworth                                     Vice  president  and  general  counsel  of  Contran,  Dixie
                                                          Holding,  Dixie Rice,  National,  NOA, Southwest,  TGI, VGI
                                                          and  Valhi;  general  counsel  of  the  Foundation,   CompX
                                                          International  Inc., a manufacturer  of ergonomic  computer
                                                          support   systems,   precision   ball  bearing  slides  and
                                                          security  products that is affiliated with Valhi ("CompX"),
                                                          and The Combined  Master  Retirement  Trust,  a trust Valhi
                                                          established to permit the  collective  investment by master
                                                          trusts  that  maintain  the  assets  of  certain   employee
                                                          benefit  plans  Valhi  and  related  companies  adopt  (the
                                                          "CMRT");   and   acting   general   counsel   of   Keystone
                                                          Consolidated Industries, Inc. ("Keystone"),  a manufacturer
                                                          of steel rod,  wire and wire  products  that is  affiliated
                                                          with Contran.

Keith A. Johnson                                          Controller of the Foundation.

William J. Lindquist                                      Director and senior vice president of Contran, Dixie Holding,
                                                          National, NOA, TGI and VGI; senior vice president of Dixie
                                                          Rice, Southwest and Valhi.

A. Andrew R. Louis                                        Secretary of Contran,  CompX,  Dixie  Holding,  Dixie Rice,
                                                          National, NOA, Southwest, TGI, VGI and Valhi.

Kelly D. Luttmer                                          Tax director of Contran, CompX, Dixie Holding, Dixie Rice,
                                                          National, NOA, Southwest, TGI, VGI and Valhi.

Ann Manix (5)                                             Managing  partner  of  Drucker  Research   Corporation,   a
                                                          privately  held  industrial  research firm; and director of
                                                          NL.

J. Landis Martin (6)                                      President,  chief  executive  officer and a director of NL;
                                                          president   of  TRE   Holdings;   chairman  of  the  board,
                                                          president   and  chief   executive   officer   of   Tremont
                                                          Corporation    (the    "Company")   and   Titanium   Metals
                                                          Corporation,  a producer of titanium metal products that is
                                                          affiliated with the Company ("TIMET").

Andrew McCollam, Jr. (7)                                  President  and a director of  Southwest;  director of Dixie
                                                          Rice; and a private investor.

Harold M. Mire (8)                                        Vice president of Dixie Rice and Southwest.

Bobby D. O'Brien                                          Vice president and treasurer of Contran, Dixie Holding, Dixie
                                                          Rice, National, NOA, TGI, VGI and Valhi; and vice president of
                                                          Southwest.

George E. Poston (9)                                      President  of Poston  Real  Estate  Co., a  privately  held
                                                          commercial  real  estate  investment  company,  and  Poston
                                                          Capital  Co., a  privately  held  investment  company;  and
                                                          director of NL.

Glenn R. Simmons                                          Vice chairman of the board of Contran, Dixie Holding, National,
                                                          NOA, TGI, VGI and Valhi; chairman of the board of CompX and
                                                          Keystone; director and executive vice president of Southwest
                                                          and Dixie Rice; and a director of NL, the Company and TIMET.

Harold C. Simmons                                         Chairman of the board and chief executive officer of Contran,
                                                          Dixie Holding, Dixie Rice, the Foundation, National, NOA,
                                                          Southwest, TGI, VGI and Valhi; chairman of the board of NL;
                                                          director of the Company; and trustee and member of the
                                                          trust investment committee of the CMRT.

Richard A. Smith (8)                                      Vice president of Dixie Rice.

Thomas P. Stafford (10)                                   Co-founder   of  Stafford,   Burke  and  Hecker,   Inc.,  a
                                                          consulting company;  director of NL, the Company and TIMET;
                                                          and a director of CMI Corporation and The Wackenhut Corp.

Gregory M. Swalwell                                       Vice president and controller of Contran, Dixie Holding,
                                                          National, NOA, TGI, VGI and Valhi; and vice president of
                                                          Dixie Rice and Southwest.

J. Walter Tucker, Jr. (11)                                President,  treasurer  and a director  of Tucker & Branham,
                                                          Inc.,  a  mortgage  banking,   insurance  and  real  estate
                                                          company;   vice  chairman  of  the  board  of  Keystone;  a
                                                          director  of Valhi;  and a member  of the trust  investment
                                                          committee of the CMRT.

Steven L. Watson                                          Director and president of Contran, Dixie Holding, National, NOA,
                                                          TGI, VGI and Valhi;director and executive vice president of
                                                          Dixie Rice and Southwest; director, vice president and
                                                          secretary of the Foundation; and a director of the
                                                          Company, NL and TIMET.

Lawrence A. Wigdor (3)                                    Executive vice president of NL.

----------

(1)      The  principal  business  address for Dr.  Barry is Southern  Methodist
         University, Perkins Administration Bldg. #224, Dallas, Texas 75275.

(2)      The principal  business address for Mr. Edelcup is 8181 Southwest 117th
         Street, Pinecrest, Florida 33156.

(3)      The principal business address for Messrs.  Garten, Hardy and Wigdor is
         Two Greenspoint  Plaza,  16825 Northchase Drive,  Suite 1200,  Houston,
         Texas 77060.

(4)      The principal  business address for Mr. Hardin is 229 Peachtree Street,
         N.E., Suite 2700, Atlanta, Georgia 30303.

(5)      The principal  business  address for Ms. Manix is 6905 Telegraph  Road,
         Suite 300, Bloomfield Hills, Michigan 48301.

(6)      The principal  business address for Mr. Martin is 1999 Broadway,  Suite
         4300, Denver, Colorado 80202.

(7)      The principal  business  address for Mr.  McCollam is 402 Canal Street,
         Houma, Louisiana 70360.

(8)      The  principal  business  address  for  Messrs.  Mire and  Smith is 600
         Pasquiere Street, Gueydan, Louisiana 70542-0010.

(9)      The  principal  business  address  for Mr.  Poston is 3407  North  Hall
         Street, Dallas, Texas 75219.

(10)     The  principal  business  address  for Gen.  Stafford  is 1006  Cameron
         Street, Alexandria, Virginia 22314.

(11)     The  principal  business  address  for  Mr.  Tucker  is 400 E.  Central
         Boulevard, Orlando, Florida 32801.






                                   SCHEDULE C

         Schedule C is hereby amended and restated as follows:

         Based upon ownership  filings with the  Commission or upon  information
provided by the persons listed on Schedule B to this Statement, such persons may
be deemed to personally beneficially own Shares, as outlined below:



                                                           Shares                  Options
                       Name                                 Held                   Held (1)                Total
            --------------------------                  -----------               -----------           -----------
                                                                                                 
Eugene K. Anderson                                              -0-                     -0-                  -0-

Thomas E. Barry                                                 -0-                     -0-                  -0-

Norman S. Edelcup                                               -0-                     -0-                  -0-

Lisa Simmons Epstein                                            298                     -0-                  298

David B. Garten                                                 -0-                     -0-                  -0-

Edward J. Hardin                                                -0-                     -0-                  -0-

Robert D. Hardy                                                 -0-                     -0-                  -0-

J. Mark Hollingsworth                                           -0-                     -0-                  -0-

Keith A. Johnson                                                -0-                     -0-                  -0-

William J. Lindquist                                            -0-                     -0-                  -0-

A. Andrew R. Louis                                              -0-                     -0-                  -0-

Kelly D. Luttmer                                                -0-                     -0-                  -0-

Ann Manix                                                       -0-                     -0-                  -0-

J. Landis Martin (2)                                         20,788                     -0-               20,788

Andrew McCollam, Jr.                                            -0-                     -0-                  -0-

Harold M. Mire                                                  -0-                     -0-                  -0-

Bobby D. O'Brien                                                -0-                     -0-                  -0-

George E. Poston                                                -0-                     -0-                  -0-

Glenn R. Simmons                                                 19                     -0-                   19

Harold C. Simmons (2)                                           -0-                     -0-                  -0-

Richard A. Smith                                                -0-                     -0-                  -0-

Thomas P. Stafford                                              -0-                   4,000                4,000

Gregory M. Swalwell                                             -0-                     -0-                  -0-

J. Walter Tucker, Jr. (3)                                       875                     -0-                  -0-

Steven L. Watson                                              4,474                     -0-                4,474

Lawrence A. Wigdor                                              -0-                     -0-                  -0-

----------

(1)      Represents  Shares  issuable  pursuant to the exercise of stock options
         within 60 days of the date of this Statement.

(2)      Mr. Simmons may be deemed to possess indirect  beneficial  ownership of
         the Shares as described  in Item 5(a) of this  Statement.  Mr.  Simmons
         disclaims beneficial ownership of all Shares.

(3)      Includes 525 Shares  directly held by a corporation of which Mr. Tucker
         is the sole stockholder.





                                  Exhibit Index

Exhibit  1        Credit  Agreement  dated as of November 6, 1998 among Valhi,
                  Inc., the financial  institutions from time to time that are a
                  party thereto and Societe  Generale,  Southwest Agency, as the
                  administrative agent, issuing bank and arranger  (incorporated
                  by reference to Exhibit 1 to Amendment  No. 59 to the Schedule
                  13D  filed  on  November  23,  1999  with the  Securities  and
                  Exchange Commission by Tremont Corporation,  Valmont Insurance
                  Company,  Valhi, Inc., Valhi Group, Inc., National City Lines,
                  Inc.,   NOA,   Inc.,   Dixie  Holding   Company,   Dixie  Rice
                  Agricultural  Corporation,   Inc.,  Southwest  Louisiana  Land
                  Company,  Inc.,  Contran  Corporation,   The  Combined  Master
                  Retirement  Trust,  the Harold  Simmons  Foundation,  Inc. and
                  Harold C. Simmons with respect to the common stock,  par value
                  $0.125 per share, of NL Industries, Inc.).

Exhibit  2        First Amendment Agreement dated as of November 5, 1999 among
                  Valhi, Inc., the financial institutions from time to time that
                  are a party thereto and Societe Generale, Southwest Agency, as
                  the   administrative   agent,   issuing   bank  and   arranger
                  (incorporated by reference to Exhibit 2 to Amendment No. 60 to
                  the   Schedule  13D  filed  on  December  14,  1999  with  the
                  Securities  and Exchange  Commission  by Tremont  Corporation,
                  Valmont Insurance  Company,  Valhi,  Inc., Valhi Group,  Inc.,
                  National City Lines,  Inc., NOA, Inc.,  Dixie Holding Company,
                  Dixie Rice Agricultural Corporation, Inc., Southwest Louisiana
                  Land Company,  Inc., Contran Corporation,  The Combined Master
                  Retirement  Trust,  the Harold  Simmons  Foundation,  Inc. and
                  Harold C. Simmons with respect to the common stock,  par value
                  $0.125 per share, of NL Industries, Inc.).

Exhibit  3        Second  Amendment  Agreement  dated as of  November  3, 2000
                  among Valhi,  Inc.,  the financial  institutions  from time to
                  time  that  are  a  party   thereto  and  U.S.  Bank  National
                  Association  as the  administrative  agent,  issuing  bank and
                  arranger  (incorporated by reference to Exhibit 3 to Amendment
                  No. 15 to this Statement).

Exhibit  4        Form of  Accession  Agreement  dated as of  December 1, 2000
                  among  Valhi,   Inc.,   the  Banks  and  U.S.   Bank  National
                  Association, as the administrative agent of the banks, and the
                  related  promissory note in the original  principal  amount of
                  $5.0  million  payable  to the  order  of Texas  Capital  Bank
                  (incorporated by reference to Exhibit 4 to Amendment No. 63 to
                  the  Schedule  13D  filed  on  September  25,  2001  with  the
                  Securities  and Exchange  Commission  by Tremont  Corporation,
                  Tremont Group, Inc., Tremont Holdings, LLC, Valhi, Inc., Valhi
                  Group,  Inc.,  National City Lines,  Inc.,  NOA,  Inc.,  Dixie
                  Holding Company,  Dixie Rice Agricultural  Corporation,  Inc.,
                  Southwest Louisiana Land Company,  Inc., Contran  Corporation,
                  The  Combined  Master  Retirement  Trust,  the Harold  Simmons
                  Foundation,  Inc.  and Harold C.  Simmons  with respect to the
                  common stock,  par value $0.125 per share,  of NL  Industries,
                  Inc.).

Exhibit  5        Stock  Purchase  Agreement  dated  as of  November  7,  2000
                  between  Valhi,  Inc. and J. Landis  Martin  (incorporated  by
                  reference to Exhibit 4 to Amendment No. 16 to this Statement).

Exhibit  6        Certificate  of  Incorporation   of  Tremont  Group,   Inc.
                  (incorporated by reference to Exhibit 5 to Amendment No. 17 to
                  this Statement).

Exhibit  7        Voting  Agreement  dated as of  December  31,  2000  between
                  Valhi,  Inc.  and  Tremont  Holdings,   LLC  (incorporated  by
                  reference to Exhibit 6 to Amendment No. 17 to this Statement).

Exhibit  8        Letter dated July 26, 2002 from Valhi,  Inc. to the board of
                  directors of Tremont Corporation (incorporated by reference to
                  Exhibit 99.1 to the Current Report on Form 8-K of Valhi,  Inc.
                  the date of event of which is July 26, 2002).

Exhibit  9        Press   Release   of  Valhi  Inc.   dated  July  26,   2002
                  (incorporated  by  reference  to Exhibit  99.2 to the  Current
                  Report on Form 8-K of Valhi,  Inc.  the date of event of which
                  is July 26, 2002).

Exhibit  10*      Press Release of Tremont Corporation dated July 29, 2002.

----------

*      Filed herewith.