UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13D

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 6)*


                      Universal Compression Holdings, Inc.
--------------------------------------------------------------------------------
                                (Name of Issuer)


                                  Common Stock
--------------------------------------------------------------------------------
                         (Title of Class of Securities)


                                   913431 10 2
                     ---------------------------------------
                                 (CUSIP Number)


                                 Burt M. Martin
                         Weatherford International, Inc.
                        515 Post Oak Boulevard, Suite 600
                              Houston, Texas 77027
                                 (713) 693-4000
--------------------------------------------------------------------------------
          (Name, Address and Telephone Number of Person Authorized to
                      Receive Notices and Communications)


                                  June 25, 2004
                     ---------------------------------------
             (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 which is the subject of this Schedule 13D, and is filing this
schedule because of Section240.13d-1(e),Section240.13d-1(f) or
Section240.13d-1(g), check the following box [ ].

NOTE: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7 for other parties
to whom copies are to be sent.

*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).


                                   Page 1 of 6



                                  SCHEDULE 13D

CUSIP NO. 9134341 10 2
--------------------------------------------------------------------------------
1      NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Weatherford International Ltd.
--------------------------------------------------------------------------------
2      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                (A) [ ]
                                                                        (B) [X]
--------------------------------------------------------------------------------
3      SEC USE ONLY

--------------------------------------------------------------------------------
4      SOURCE OF FUNDS*

       OO
--------------------------------------------------------------------------------
5      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO
       ITEMS 2(o) OR  2(E)                                                  [ ]

--------------------------------------------------------------------------------
6      CITIZENSHIP OR PLACE OF ORGANIZATION

       Bermuda
--------------------------------------------------------------------------------
      NUMBER OF       7     SOLE VOTING POWER
       SHARES
    BENEFICIALLY            10,750,000 shares
      OWNED BY        ----------------------------------------------------------
        EACH          8     SHARED VOTING POWER
      REPORTING
       PERSON               -0-
        WITH          ----------------------------------------------------------
                      9     SOLE DISPOSITIVE POWER

                            10,750,000 shares
                      ----------------------------------------------------------
                      10    SHARED DISPOSITIVE POWER

                            -0-
--------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      10,750,000 shares

--------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]
--------------------------------------------------------------------------------
13     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

       34%
       (based on Annual Report on Form 10-K filed by the Issuer in June 2004)
--------------------------------------------------------------------------------
14     TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------
                      *SEE INSTRUCTIONS BEFORE FILLING OUT


                                   Page 2 of 6




                                  SCHEDULE 13D

CUSIP NO. 9134341 10 2
--------------------------------------------------------------------------------
1      NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Weatherford International, Inc.
--------------------------------------------------------------------------------
2      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                (A) [ ]
                                                                        (B) [X]
--------------------------------------------------------------------------------
3      SEC USE ONLY

--------------------------------------------------------------------------------
4      SOURCE OF FUNDS*

       OO
--------------------------------------------------------------------------------
5      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO
       ITEMS 2(o) OR  2(E)                                                  [ ]
--------------------------------------------------------------------------------
6      CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware

--------------------------------------------------------------------------------
      NUMBER OF       7     SOLE VOTING POWER
       SHARES
    BENEFICIALLY            -0-
      OWNED BY        ----------------------------------------------------------
        EACH          8     SHARED VOTING POWER
      REPORTING
       PERSON               -0-
        WITH          ----------------------------------------------------------
                      9     SOLE DISPOSITIVE POWER

                            -0-
                      ----------------------------------------------------------
                      10    SHARED DISPOSITIVE POWER

                            -0-
--------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      -0-

--------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                             [ ]

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

       0%

--------------------------------------------------------------------------------
14     TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------
                      *SEE INSTRUCTIONS BEFORE FILLING OUT


                                   Page 3 of 6




                                  SCHEDULE 13D

CUSIP NO. 9134341 10 2
--------------------------------------------------------------------------------
1      NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       WEUS Holding, Inc.
--------------------------------------------------------------------------------
2      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                (A) [ ]
                                                                        (B) [X]
--------------------------------------------------------------------------------
3      SEC USE ONLY

--------------------------------------------------------------------------------
4      SOURCE OF FUNDS*

       OO
--------------------------------------------------------------------------------
5      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO
       ITEMS 2(o) OR  2(E)                                                  [ ]
--------------------------------------------------------------------------------
6      CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware
--------------------------------------------------------------------------------
      NUMBER OF       7     SOLE VOTING POWER
       SHARES
    BENEFICIALLY            -0-
      OWNED BY        ----------------------------------------------------------
        EACH          8     SHARED VOTING POWER
      REPORTING
       PERSON               -0-
        WITH          ----------------------------------------------------------
                      9     SOLE DISPOSITIVE POWER

                            -0-
                      ----------------------------------------------------------
                      10    SHARED DISPOSITIVE POWER

                            -0-
--------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      -0-
--------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                            [ ]
--------------------------------------------------------------------------------
13     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

       0%
--------------------------------------------------------------------------------
14     TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------
                      *SEE INSTRUCTIONS BEFORE FILLING OUT


                                   Page 4 of 6




      This Amendment No. 6 (this "Amendment No. 6") to the Statement on Schedule
13D filed on November 2, 2000, as amended by Amendment No. 1 filed on November
3, 2000, Amendment No. 2 filed on February 14, 2001, Amendment No. 3 filed on
December 10, 2001, Amendment No. 4 filed on July 2, 2002 and Amendment No. 5
filed on April 23, 2004 (collectively, the "Statement"), relates to the
beneficial ownership of shares of common stock, par value $0.01 per share
("Universal Common Stock"), of Universal Compression Holdings, Inc.
("Universal"). The address of Universal's principal executive offices is 4440
Brittmoore Road, Houston, Texas 77041.

      This Amendment No. 6 is being filed by Weatherford International Ltd., a
Bermuda exempted company ("Weatherford Bermuda"), Weatherford International,
Inc., a Delaware corporation and a wholly owned subsidiary of Weatherford
Bermuda ("Weatherford Delaware"), and WEUS Holding, Inc., a Delaware corporation
and a wholly owned subsidiary of Weatherford Delaware ("WEUS") (each
individually a "Reporting Person" and together, the "Reporting Persons") to
amend Items 5 of the Statement. Capitalized terms not defined herein shall have
the meanings ascribed to them in the Statement.

ITEM 5. INTEREST IN SECURITIES OF THE ISSUER

      Section (a) of Item 5 of the Statement is hereby amended to replace the
second paragraph as follows:

      The aggregate 10,750,000 shares of Universal Common Stock that the
Reporting Persons may be deemed to beneficially own represent approximately 34%
of the outstanding shares of Universal Common Stock.

      Section (b) of Item 5 of the Statement is hereby amended and restated in
its entirety to read as follows:

      (b) The number of shares of Universal Common Stock as to which there is
sole power to vote or direct the vote, shared power to vote or direct the vote,
sole power to dispose or direct the disposition, or shared power to dispose or
direct the disposition for each Reporting Person is set forth on the cover pages
of this Amendment No. 6, and such information is incorporated herein by
reference.

      The Reporting Persons may be deemed to have the sole power to vote or
direct the voting of up to 10,750,000 shares of Universal Common Stock, which
amount is equal to 34% of the shares of Universal Common Stock outstanding based
upon Universal's Annual Report on Form 10-k filed in June 2004.

      The Reporting Persons may be deemed to have the sole power to dispose of
or direct the disposition of all 10,750,000 shares of Universal Common Stock and
will not share the power to dispose of or direct the disposition of such shares
with any other person.

      Section (c) of Item 5 of the Statement is hereby amended in its entirety
to read as follows:


                                   Page 5 of 6


      (c) Weatherford Bermuda sold 3,000,000 shares of Universal Common Stock on
the New York Stock Exchange at $30.05 per share with a settlement date of
June 25, 2004.

                                   SIGNATURES

      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.

Dated: June 29, 2004


                        WEATHERFORD INTERNATIONAL LTD.

                        By:    /s/  Burt M. Martin
                               -------------------------------------------------
                        Name:  Burt M. Martin
                        Title: Senior Vice President, General Counsel and
                               Secretary

                        WEATHERFORD INTERNATIONAL, INC.

                        By:    /s/  Burt M. Martin
                               -------------------------------------------------
                        Name:  Burt M. Martin
                        Title: Senior Vice President, General Counsel and
                               Secretary

                        WEUS HOLDING, INC.

                        By:    /s/  Burt M. Martin
                               -------------------------------------------------
                        Name:  Burt M. Martin
                        Title: Assistant Secretary


                                   Page 6 of 6