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

                                  SCHEDULE 13D

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 5)*


                      Universal Compression Holdings, Inc.
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                                (Name of Issuer)

                                  Common Stock
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                         (Title of Class of Securities)

                                   913431 10 2
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                                 (CUSIP Number)


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

                                  April 2, 2004
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             (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 Section 240.13d-1(e), Section 240.13d-1(f) or Section
240.13d-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 12



                                  SCHEDULE 13D

-------------------------                          -----------------------------
CUSIP No.   9134341 10 2
-------------------------                          -----------------------------

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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(d) OR 2(e)                                                   [ ]

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

    Bermuda
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                7.  SOLE VOTING POWER
  NUMBER OF
                    13,750,000 shares
   SHARES      -----------------------------------------------------------------
                8.  SHARED VOTING POWER
BENEFICIALLY
                    -0-
OWNED BY EACH  -----------------------------------------------------------------
                9.  SOLE DISPOSITIVE POWER
  REPORTING
                    13,750,000 shares
   PERSON      -----------------------------------------------------------------
               10.  SHARED DISPOSITIVE POWER
    WITH
                    -0-
--------------------------------------------------------------------------------
11.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     13,750,000 shares
--------------------------------------------------------------------------------
12.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
     CERTAIN SHARES*                                                        [ ]

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

     44.3% (based on Quarterly Report on Form 10-Q filed by the Issuer in
     February 2004)
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14.  TYPE OF REPORTING PERSON

     CO
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                      *SEE INSTRUCTIONS BEFORE FILLING OUT

                                  SCHEDULE 13D


                                  Page 2 of 12



                                  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(d) OR 2(e)                                                   [ ]

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

    Delaware
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                7.  SOLE VOTING POWER
  NUMBER OF
                    -0-
   SHARES      -----------------------------------------------------------------
                8.  SHARED VOTING POWER
BENEFICIALLY
                    -0-
OWNED BY EACH  -----------------------------------------------------------------
                9.  SOLE DISPOSITIVE POWER
  REPORTING
                    -0-
   PERSON      -----------------------------------------------------------------
               10.  SHARED DISPOSITIVE POWER
    WITH
                    -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 12


                                  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(d) OR 2(e)                                                   [ ]

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

    Delaware
--------------------------------------------------------------------------------
                7.  SOLE VOTING POWER
  NUMBER OF
                    -0-
   SHARES      -----------------------------------------------------------------
                8.  SHARED VOTING POWER
BENEFICIALLY
                    -0-
OWNED BY EACH  -----------------------------------------------------------------
                9.  SOLE DISPOSITIVE POWER
  REPORTING
                    -0-
   PERSON      -----------------------------------------------------------------
               10.  SHARED DISPOSITIVE POWER
    WITH
                    -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 12



ITEM 1.  SECURITY AND ISSUER.

         This Amendment No. 5 (this "Amendment No. 5") 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 and Amendment No. 4 filed on July 2, 2002
(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. 5 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 (a)
reflect Universal's filing of a shelf registration statement to register 7.0
million shares of Universal Common Stock held by Weatherford Bermuda, (b)
reflect that Weatherford Bermuda and Universal have entered into an Amended and
Restated Registration Rights Agreement (the "New Registration Rights
Agreement"), (c) terminate the reporting obligations of Weatherford Delaware and
WEUS with respect to the Statement and (d) amend Items 1, 2, 4, 6 and 7 of the
Statement. Capitalized terms not defined herein shall have the meanings ascribed
to them in the Statement.

ITEM 2.  IDENTITY AND BACKGROUND.

          Schedule I of the Statement, which contains information concerning the
executive officers and directors of Weatherford Bermuda required to be disclosed
in response to Item 2 and General Instruction C to Schedule 13D, is hereby
supplemented by Schedule I attached hereto and incorporated herein by reference.
Such executive officers and directors may be deemed, but are not conceded to be,
controlling persons of Weatherford Bermuda. No corporation or other person is or
may be deemed to be ultimately in control of Weatherford Bermuda.

          WEUS was originally a Reporting Person on the Statement because it was
the initial acquirer the shares of Universal Common Stock covered hereby. It
subsequently transferred those shares to Weatherford Bermuda, as reported on
Amendment No. 4 to the Statement. Due to the amendment and restatement of the
Registration Rights Agreement, WEUS no longer has any rights under that original
agreement and will therefore no longer be a Reporting Person under this
Schedule. Weatherford Delaware was initially included as a Reporting Person on
this Statement because of its ownership of WEUS. Weatherford Delaware will no
longer be a Reporting Person under this Schedule.


                                  Page 5 of 12






ITEM 4.  PURPOSE OF TRANSACTION

          Item 4 of the Statement is hereby amended to include the following as
the last paragraph under the heading "The Registration Rights Agreement" in such
section:

          Weatherford Bermuda and Universal have entered into an Amended and
Restated Registration Rights Agreement, as of March 23, 2004 (the "New
Registration Rights Agreement"). WEUS is not a party to the agreement. The full
text of the New Registration Rights Agreement is filed as an exhibit to the
Statement and is incorporated herein by reference.

          Item 4 of the Statement is hereby further amended to include the
following paragraph immediately after the first paragraph under the heading "The
Purchase Agreement" in such section:

          On April 2, 2004, Universal publicly announced that it had filed with
the Securities and Exchange Commission a registration statement to register 7.0
million shares of Universal Common Stock held by Weatherford Bermuda. Following
effectiveness of the registration statement, Weatherford Bermuda may offer and
sell these shares of Universal Common Stock from time to time, through public or
private transactions, at prevailing market prices or at other negotiated prices,
to be determined when and if the shares are offered. Universal is not selling
any shares of Universal Common Stock and will not receive any of the proceeds
from the sale of any such Universal Common Stock by Weatherford Bermuda.

ITEM 6.  CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
         TO SECURITIES OF THE ISSUER.

         Item 6 is hereby amended to incorporate by reference therein the New
Registration Rights Agreement.

ITEM 7.  MATERIAL TO BE FILED AS EXHIBITS

         Item 7 is hereby amended and supplemented to include the following:

         A.   Joint Filing Agreement

         B.   Amended and Restated Registration Rights Agreement, dated as of
              March 23, 2004, between Weatherford International Ltd. and
              Universal Compression Holdings, Inc. (incorporated by reference to
              Exhibit 10.1 to Registration Statement on Form S-3 (Reg. No.
              333-114145) filed by Universal Compression Holdings, Inc. on April
              2, 2004).


                                  Page 6 of 12




                                   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: April 23, 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: President and Secretary


                                  Page 7 of 12






                                   SCHEDULE I
             (Amending information previously filed with respect to
                        Weatherford International Ltd.)

                        DIRECTORS AND EXECUTIVE OFFICERS
                                       OF
                         WEATHERFORD INTERNATIONAL LTD.


         The following table sets forth the name, business address and present
principal occupation or employment of each director and executive officer of
Weatherford Bermuda. Unless otherwise indicated below, each such person is a
citizen of the United States of America and is an employee of Weatherford U.S.,
L.P., a wholly owned subsidiary of Weatherford Bermuda, and the business address
of each such person is c/o Weatherford International, Inc., 515 Post Oak
Boulevard, Suite 600, Houston, Texas 77027. During the last five years, none of
the persons listed below has been convicted in a criminal proceeding (excluding
traffic violations or similar misdemeanors), nor has any of such persons been 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.

                                 Present Principal Occupation or Employment;
Name                                          Business Address
----                         ---------------------------------------------------

Bernard J. Duroc-Danner      Chairman of the Board of Directors, President and
                             Chief Executive Officer

E. Lee Colley, III           Senior Vice President and President -- Completion
                             and Production Systems

Gary L. Warren               Senior Vice President and President -- Drilling and
                             Well Services

Stuart E. Ferguson           Senior Vice President and Chief Technology Officer

Burt M. Martin               Senior Vice President, General Counsel and
                             Secretary

Jon R. Nicholson             Senior Vice President -- Human Resources

Lisa W. Rodriguez            Senior Vice President and Chief Financial Officer

M. David Colley              Vice President - Global Manufacturing

Keith R. Morley              Vice President - Enterprise Excellence


                                  Page 8 of 12


James N. Parmigiano          Vice President -- Operational Controller

Nicholas F. Brady            Director of Weatherford Bermuda and Chairman of
                             Darby Overseas Investments, Ltd. and Darby
                             Technology Ventures Group, LLC, investment firms
                                        16 North Washington Street
                                        P.O. Box 1410
                                        Easton, MD 21601

Philip Burguieres            Director of Weatherford Bermuda, Vice Chairman and
                             part owner of The Houston Texans, and Chief
                             Executive Officer of EMC Holdings, LLC, a private
                             energy investment firm
                                        Reliant Stadium
                                        Two Reliant Park
                                        Houston, TX 77054

David J. Butters             Director of Weatherford Bermuda and a Managing
                             Director of Lehman Brothers Inc., an investment
                             banking company
                                        Lehman Brothers Inc.
                                        399 Park Avenue, 9th Floor
                                        New York, New York 10022

Sheldon B. Lubar             Director of Weatherford Bermuda and Chairman of
                             Lubar & Co., a private investment and management
                             company
                                        Lubar & Company
                                        700 North Water St., #1200
                                        Milwaukee, Wisconsin 53202

William Macaulay             Director of Weatherford Bermuda and Chairman and
                             Chief Executive Officer of First Reserve
                             Corporation, a private equity investment firm
                                        First Reserve Corporation
                                        One Lafayette Place
                                        Greenwich, Connecticut 06830


                                  Page 9 of 12




Robert B. Millard            Director of Weatherford Bermuda and a Managing
                             Director of Lehman Brothers Inc., an investment
                             banking company
                                        Lehman Brothers Inc.
                                        399 Park Avenue, 9th Floor
                                        New York, New York 10022

Robert K. Moses, Jr.         Director of Weatherford Bermuda and a private
                             investor, principally in the oil and gas
                             exploration and oilfield services business in
                             Houston, Texas
                                        Black Jack Resources, Inc.
                                        1220 Augusta, #240
                                        Houston, Texas 77057

The Honorable
Robert A. Rayne              Director of Weatherford Bermuda and Chief Executive
                             Director of London Merchant Securities plc, a
                             United Kingdom-listed public limited company
                             engaged in property and venture/development capital
                             investment
                                        London Merchant Securities plc
                                        33 Robert Adam Street
                                        London W1U 3HR England
                                        Mr. Rayne is a citizen of the U.K.


                                  Page 10 of 12



                                  EXHIBIT INDEX


          A.   Joint Filing Agreement

          B.   Amended and Restated Registration Rights Agreement, dated as of
               March 23, 2004, between Weatherford International Ltd. and
               Universal Compression Holdings, Inc. (incorporated by reference
               to Exhibit 10.1 to Registration Statement on Form S-3 (Reg. No.
               333-114145) filed by Universal Compression Holdings, Inc. on
               April 2, 2004).


                                  Page 11 of 12