SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  Schedule 13D
                               (Amendment No. 18)*

                    Under the Securities Exchange Act of 1934


                           TITANIUM METALS CORPORATION
                                (Name of Issuer)

                     Common Stock, $0.01 par value per share
                         (Title of Class of Securities)

                                   888339 10 8
                                 (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)

                                   May 5, 2003
                      (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.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Tremont LLC

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

             (a)  [   ]

             (b)  [ X ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC and AF

     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                                     1,261,850
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,261,850

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,261,850

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Valhi, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Valhi Group, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      National City Lines, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      NOA, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Dixie Holding Company

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Dixie Rice Agricultural Corporation, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Southwest Louisiana Land Company, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Contran Corporation

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,357,380
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,357,380

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,357,380

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

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

                      41.5%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Harold Simmons Foundation, Inc.

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,263,650
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,263,650

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,263,650

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

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

                      39.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      The Combined Master Retirement Trust

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

             (a)  [   ]

             (b)  [ X ]

     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

                      Texas

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     1,550,170
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,550,170

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      1,550,170

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

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

                      48.7%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      EP






CUSIP No.  888339 10 8

     1       NAMES OF REPORTING PERSONS AND I.R.S. IDENTIFICATION NOS. OF SUCH
             PERSONS (ENTITIES ONLY)

                      Harold C. Simmons

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

             (a)  [   ]

             (b)  [ X ]

     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                                     1,648,660
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      1,648,660

    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. 18
                                 TO SCHEDULE 13D

         This amended statement on Schedule 13D (collectively, this "Statement")
relates  to the  common  stock,  $0.01 par value per share  (the  "Shares"),  of
Titanium Metals Corporation, a Delaware corporation (the "Company"). Items 2, 3,
4, 5 and 7 of this Statement are hereby amended as set forth below.

Item 2.  Identity and Background.

         Item 2(a) is amended and restated as follows:

         (a)  The  following  entities  or  person  are  filing  this  Statement
(collectively, the "Reporting Persons"):

                  (i) Tremont LLC and The Combined Master  Retirement Trust (the
         "CMRT") as direct holders of Shares;

                  (ii)  Valhi,  Inc.  ("Valhi"),   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") and the Harold Simmons
         Foundation,  Inc.  (the  "Foundation")  by virtue of their  direct  and
         indirect  ownership of securities of Tremont LLC (as described below in
         this Statement); and

                  (iii)  Harold  C.  Simmons  by virtue  of his  positions  with
         Contran  and  certain  of the  other  entities  (as  described  in this
         Statement).

By signing this Statement, each Reporting Person agrees that this Statement is
filed on its or his behalf.

         Tremont LLC, the CMRT and Valhi are the direct holders of approximately
39.7%, 9.0% and 0.1%,  respectively,  of the 3,180,182 Shares  outstanding as of
May 7, 2003  according to the  Company's  Quarterly  Report on Form 10-Q for the
quarter  ended March 31,  2003 (the  "Outstanding  Shares").  Tremont LLC may be
deemed to control the Company.

         Harold  C.  Simmons'  spouse,  by  virtue of her  direct  ownership  of
1,000,000  6  5/8%  Convertible  Preferred   Securities,   Beneficial  Unsecured
Convertible  Securities  of the  TIMET  Capital  Trust 1 (the  "BUCs")  that are
convertible  into 133,900 Shares,  indirectly  holds  approximately  4.0% of the
outstanding  Shares,  assuming the full conversion of only the BUCs she directly
holds.

         In addition to Shares  Tremont LLC and Valhi directly hold that Contran
may be deemed to indirectly own,  Contran,  by virtue of its direct ownership of
700,000  BUCs  that  are  convertible  into  93,730  Shares,   indirectly  holds
approximately  2.9% of the outstanding  Shares,  assuming the full conversion of
only the BUCs Contran directly holds.

         Valhi  is the  direct  holder  of  100% of the  outstanding  membership
interests  of  Tremont  LLC and may be  deemed  to  control  Tremont  LLC.  VGI,
National, Contran, the Foundation, the Contran Deferred Compensation Trust No. 2
(the  "CDCT No. 2") and the CMRT are the direct  holders of 77.6%,  9.1%,  2.9%,
1.3%, 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 CMRT directly holds  approximately  9.0% of the Outstanding  Shares
and 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.

         The Foundation  directly holds  approximately  1.3% 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 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
owes 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.

         Valmont Insurance Company ("Valmont"), NL Industries, Inc. ("NL") and a
subsidiary of NL directly own 1,000,000  shares,  3,522,967 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.
Valhi and Tremont LLC are the direct  holders of 63.2% and 21.4%,  respectively,
of the  outstanding  common stock of NL.  Together  Valhi and Tremont LLC may be
deemed to control NL. Pursuant to Delaware law, Valhi treats the shares of Valhi
common stock that Valmont, NL and the subsidiary of NL own as treasury stock for
voting  purposes  and for the purposes of this report such shares are not deemed
outstanding.

         Mr.  Harold C.  Simmons is  chairman of the board of Tremont  LLC,  NL,
Valhi, VGI, National, NOA, Dixie Holding, Dixie Rice, Southwest and Contran.

         By virtue of the offices held, the stock  ownership and his services 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.  Mr. Simmons disclaims  beneficial  ownership of
the Shares beneficially owned, directly or indirectly, by any of such entities.

         Harold C.  Simmons  and his spouse are  co-trustees  of a trust for the
benefit of the grandchildren of his spouse (the  "Grandchildren's  Trust").  The
Grandchildren's  Trust is the direct holder of 4,760  Shares.  Mr.  Simmons,  as
co-trustee of the  Grandchildren's  Trust,  has the power to vote and direct the
disposition of the Shares the Grandchildren's  Trust directly holds. Mr. Simmons
disclaims  beneficial  ownership  of any Shares that the  Grandchildren's  Trust
holds.

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

         Item 3 is amended as follows:

         The total amount of funds Valhi used to acquire the Shares purchased by
it as reported in Item 5(c) was $35,835.00 (including  commissions).  Such funds
were provided by Valhi's cash on hand.

         The  Reporting  Persons  understand  that the total amount of funds the
Grandchildren's  Trust used to acquire the Shares purchased by it as reported in
Item 5(c) was $69,320.23  (including  commissions).  Such funds were provided by
the Grandchildren's Trust's cash on hand.

         On May 5, 2003,  Valhi  commenced  a tender  offer  (the  "BUCs  Tender
Offer") to purchase for cash up to 1,000,000 BUCs for a purchase price of $10.00
per BUC. The BUCs  include the  associated  guarantee  by the Company.  The BUCs
Tender Offer expires at 12:00 midnight,  New York City time, on Monday,  June 2,
2003,  unless  extended.  The  description  of the  BUCs  Tender  Offer  in this
Statement is qualified in its entirety by the Schedule TO and its exhibits  that
Valhi filed with the  Securities and Exchange  Commission  (the "SEC") on May 5,
2003, as amended by Amendment No. 1 to Schedule TO that Valhi filed with the SEC
on May 16, 2003,  as such  Schedule TO may be further  amended from time to time
(collectively,  the "Schedule TO"), which Schedule TO is incorporated  herein by
reference.  For a description of the amount and source of funds Valhi intends to
use to purchase BUCS in the BUCs Tender Offer, see the Schedule TO.

Item 4.  Purpose of Transaction

         No change to Item 4 except for the addition of the following:

         For a  description  of the  purpose of the BUCs Tender  Offer,  see the
Schedule TO, which is incorporated herein by reference.

         Depending  upon  their   evaluation  of  the  Company's   business  and
prospects,  and  upon  future  developments  (including,  but  not  limited  to,
performance of the Company's  securities in the market,  availability  of funds,
alternative  uses of funds, the Reporting  Persons' tax planning  objectives and
cash needs, 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  Company  securities,  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
Company  securities  held by such entity or person,  or cease  buying or selling
Company securities. Any such additional purchases or sales of Company securities
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.

Item 5.  Interest in Securities of the Issuer.

         Item 5 is amended as follows:

         No change except for the addition of the following:

         (a) Tremont LLC, the CMRT, the Grandchildren's  Trust and Valhi are the
direct  holders of  1,261,850  Shares,  286,520  Shares,  4,760 Shares and 1,800
Shares, respectively.  Harold Simmons' spouse and Contran are the direct holders
of 1,000,000 BUCs and 700,000 BUCs,  respectively,  which are  convertible  into
133,900 Shares and 93,730 Shares, respectively.

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

                  (1) Valhi,  VGI,  National,  NOA, Dixie  Holding,  Dixie Rice,
         Southwest and the  Foundation  may each be deemed to be the  beneficial
         owner of the 1,263,650 Shares  (approximately  39.7% of the Outstanding
         Shares) that Tremont LLC and Valhi hold directly;

                  (2)  Contran may be deemed to be the  beneficial  owner of the
         1,263,650  Shares  that  Tremont  LLC and Valhi hold  directly  and the
         93,730 Shares  Contran may acquire upon  conversion of the 700,000 BUCs
         that Contran holds  directly (in the  aggregate  1,357,380  Shares,  or
         approximately  41.5%  of  the  outstanding  Shares  assuming  the  full
         conversion of only Contran's BUCs);

                  (3) The CMRT may be deemed to be the  beneficial  owner of the
         1,550,170 Shares  (approximately  48.7% of the Outstanding Shares) that
         Tremont LLC, Valhi and the CMRT hold directly; and

                  (4) Harold C. Simmons may be deemed to be the beneficial owner
         of the 1,554,930 Shares that Tremont LLC, the CMRT, the Grandchildren's
         Trust and Valhi hold directly and the 93,730 Shares Contran may acquire
         upon conversion of the 700,000 BUCs that Contran holds directly (in the
         aggregate  1,648,660 Shares, or approximately  50.4% of the outstanding
         Shares assuming the full  conversion of only the BUCs Contran  directly
         holds).

         Mr. Simmons disclaims beneficial ownership of all Company securities.

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

                  (1) Valhi,  VGI,  National,  NOA, Dixie  Holding,  Dixie Rice,
         Southwest and the  Foundation  may each be deemed to share the power to
         vote and direct the disposition of the 1,263,650 Shares  (approximately
         39.7% of the  Outstanding  Shares)  that  Tremont  LLC and  Valhi  hold
         directly;

                  (2)  Contran  may be  deemed  to share  the  power to vote and
         direct the  disposition  of the  1,263,650  Shares that Tremont LLC and
         Valhi hold  directly  and the 93,730  Shares  Contran may acquire  upon
         conversion  of the 700,000  BUCs that  Contran  holds  directly (in the
         aggregate  1,357,380 Shares, or approximately  41.5% of the outstanding
         Shares assuming the full conversion of only Contran's BUCs);

                  (3) The CMRT may be  deemed  to  share  the  power to vote and
         direct the disposition of the 1,550,170 Shares  (approximately 48.7% of
         the  Outstanding  Shares)  that  Tremont  LLC,  Valhi and the CMRT hold
         directly; and

                  (4) Harold C. Simmons may be deemed to share the power to vote
         and direct the  disposition  of the 1,554,930  Shares that Tremont LLC,
         the CMRT,  the  Grandchildren's  Trust and Valhi hold  directly and the
         93,730 Shares  Contran may acquire upon  conversion of the 700,000 BUCs
         that Contran holds  directly (in the  aggregate  1,648,660  Shares,  or
         approximately  50.4%  of  the  outstanding  Shares  assuming  the  full
         conversion of only the BUCs Contran directly holds).

         (c) The table  below sets forth  purchases  of Shares by the  Reporting
Persons and the  Grandchildren's  Trust since March 6, 2003, sixty days prior to
the date that requires the filing of this Statement. All purchases were executed
on the New York Stock Exchange.




                                                                Type of                          Price Per Security
                                                                Company             Numbers        (exclusive of
                  Purchaser                      Date           Security         of Securities     commissions)
--------------------------------------------   --------         --------         -------------  -------------------
                                                                                          
Valhi, Inc...................................  03/07/03         Shares               500              $19.7500
Valhi, Inc...................................  03/07/03         Shares             1,300              $19.9000
Grandchildren's Trust .......................  04/21/03         Shares             1,300              $21.5692
Grandchildren's Trust ........................ 04/22/03         Shares             1,900              $21.6383


         (d) Each of Tremont LLC, the CMRT, Harold C. Simmons' spouse,  Contran,
the  Grandchildren's  Trust and Valhi has the right to receive  and the power to
direct the receipt of dividends from, and proceeds from the sale of, the Company
equity securities held by such entity or person.

Item 7.  Material to be Filed as Exhibits.

         Item 7 is amended and restated in its entirety as follows:

Exhibit 1         Agreement  and Plan of Merger  dated  November  4, 2002  among
                  Valhi, Inc., Valhi Acquisition Corp. and Tremont  Corporation,
                  as amended  (incorporated  by  reference  to Appendix A to the
                  Registration Statement on Form S-4 (Reg. No. 333-101244) filed
                  by Valhi, Inc. with the Securities and Exchange  Commission on
                  November 15, 2002).

Exhibit 2         Agreement  and Plan of  Merger  dated as of  November  4, 2002
                  among Valhi,  Inc.,  Tremont Group, Inc. and Valhi Acquisition
                  Corp.  II  (incorporated  by  reference to Exhibit 10.3 to the
                  Quarterly  Report on Form 10-Q of Valhi,  Inc. for the quarter
                  ended September 30, 2002).

Exhibit 3         Schedule TO dated as of May 5, 2003 filed by Valhi,  Inc. with
                  the  Securities  and  Exchange  Commission   (incorporated  by
                  reference  to the Schedule TO dated as of May 5, 2003 filed by
                  Valhi, Inc. with the Securities and Exchange Commission).

Exhibit 4         Amendment  No. 1 to Schedule TO dated as of May 16, 2003 filed
                  by Valhi,  Inc. with the  Securities  and Exchange  Commission
                  (incorporated  by reference to Amendment No. 1 to the Schedule
                  TO dated as of May 16,  2003  filed by  Valhi,  Inc.  with the
                  Securities and Exchange Commission).






                                    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:  May 21, 2003




                                                          /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:  May 21, 2003




                                                          /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.


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 LLC
VALHI GROUP, INC.
VALHI, INC.