<PAGE>   1

                                                                   EXHIBIT 10.13

                    AMENDMENT NO. 1 TO MANAGEMENT AGREEMENT

     THIS AMENDMENT NO. 1, dated as of April 30, 2001 (the "Amendment"), to that
certain Management Agreement (as amended, restated or otherwise modified from
time to time prior to the date hereof, the "Agreement"), dated as of February 9,
2001, between Universal Compression, Inc. ( "UCI") and BRL Universal Compression
Funding I, L.P. ("BRL").

                                  WITNESSETH:

     WHEREAS, UCI and BRL desire to amend the Agreement;

     NOW THEREFORE, in consideration of the premises and mutual covenants herein
contained, the parties hereto agree as follows:

     SECTION 1. Defined Terms. Unless otherwise amended by the terms of this
Amendment terms used in this Amendment shall have the meanings assigned to them
in the Agreement.

     SECTION 2. Amendments to the Agreement. Effective at 8:00 a.m. (New York
time) on April 30, 2001, following the execution and delivery of this Amendment
(the "Effective Date"):

     (a) Section 9.12 of the Agreement is hereby amended and restated in its
entirety as follows:

     "9.12 Appraisals. (1) By not later July 16, 2001, the Manager shall (at its
expense) furnish (or cause to be furnished) to the Owner and to each Entitled
Party two (2) additional Appraisals setting forth the Appraised Value of each
Lease Pool as of the Closing Date. Upon delivery of such additional Appraisals,
the Appraised Value of each Compressor shall be adjusted in accordance with the
provisions set forth in the definition of the term "Appraised Value."

           By not later than the Payment Date in February of each calendar year
commencing on the Payment Date occurring in February, 2002, the Manager shall
(at its expense) furnish (or cause to be furnished) to the Owner and to each
Entitled Party three (3) Appraisals setting forth the Appraised Value of each
Lease Pool as of the date of such Appraisal."

     SECTION 3. Representations and Warranties. Each of the parties hereto
hereby confirms that each of the representations and warranties set forth in the
Agreement made by such party are true and correct as of the date first written
above with the same effect as though each had been made by such party as of such
date, except to the extent that any of such representations and warranties
expressly relate to earlier dates.

     SECTION 4. Effectiveness of Agreement.

     (a) This Amendment shall be binding upon and inure to the benefit of the
parties hereto and their respective successors and assigns.
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     (b) On the Effective Date, (i) this Amendment shall become a part of the
Agreement and (ii) each reference in the Agreement to "this Agreement", or
"hereof", "hereunder" or words of like import, and each reference in any other
document to the Agreement shall mean and be a reference to such Agreement, as
amended or modified hereby.

     (c) Except as expressly amended or modified hereby, the Agreement shall
remain in full force and effect and is hereby ratified and confirmed by the
parties hereto.


     SECTION 5. Execution in Counterparts, Effectiveness. This Amendment may be
executed by the parties hereto in separate counterparts, each of which shall be
deemed to be an original and all of which shall constitute together but one and
the same agreement.

     SECTION 6. Governing Law. THIS AMENDMENT SHALL BE CONSTRUED IN ACCORDANCE
WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REFERENCE TO NEW YORK'S
CONFLICTS OF LAW PRINCIPLES, AND THE OBLIGATIONS, RIGHTS AND REMEDIES OF THE
PARTIES HEREUNDER SHALL BE DETERMINED IN ACCORDANCE WITH THE LAWS OF THE STATE
OF NEW YORK.



                            [signature page follows]









                                      -2-
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     IN WITNESS WHEREOF, each of the parties hereto has caused a counterpart of
this Amendment to be duly executed and delivered as of the date hereof.


                                        UNIVERSAL COMPRESSION, INC.


                                        By:    /s/ RICHARD W. FITZGERALD
                                            ------------------------------------
                                            Name:  Richard W. Fitzgerald
                                            Title: Senior Vice President and
                                                   Chief Financial Officer



                                        UCO COMPRESSION LLC

                                        By:    /s/ RICHARD W. FITZGERALD
                                            ------------------------------------
                                            Name:  Richard W. Fitzgerald
                                            Title: Senior Vice President and
                                                   Chief Financial Officer



                                       BRL UNIVERSAL COMPRESSION FUNDING I, L.P.

                                       By: BRL UNIVERSAL COMPRESSION
                                           MANAGEMENT, INC.
                                           its general partner

                                            By:    /s/ GREGORY C. GREENE
                                                --------------------------------
                                                Name:  Gregory C. Greene
                                                Title: President


For the limited purposes set forth herein,
Accepted and Agreed:

WELLS FARGO BANK MINNESOTA, NATIONAL ASSOCIATION,
not in its individual capacity but solely as
indenture trustee



By:    /s/ EDNA BARBER
    ----------------------------------------
    Name:  Edna Barber
    Title: Assistant Vice President







           SIGNATURE PAGE TO AMENDMENT NO. 1 TO MANAGEMENT AGREEMENT
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     Amendment No. 1 to the Management Agreement is hereby approved.

                                     FIRST UNION SECURITIES, INC., as deal agent


                                     By: /s/ MANOJ KUMAR
                                        ----------------------------------------
                                         Name: Manoj Kumar
                                         Title: Vice President


                                     VARIABLE FUNDING CAPITAL
                                     CORPORATION, as note holder


                                     By: First Union Securities, Inc.,
                                         as attorney-in-fact

                                         By: /s/ DARRELL R. BABER
                                            -----------------------------------
                                             Name: Darrell R. Baber
                                             Title: Managing Director



























           SIGNATURE PAGE TO AMENDMENT NO. 1 TO MANAGEMENT AGREEMENT