<PAGE>
                                                                   EXHIBIT 10.16

                     AMENDMENT NO. 3 TO MANAGEMENT AGREEMENT

      THIS AMENDMENT NO. 3, dated as of September 14, 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 September 14, 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 September 30, 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.



Amendment No. 3 to Management Agreement-Page 1
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      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.

      (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]


Amendment No. 3 to Management Agreement-Page 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
                                              ----------------------------------
                                                  Senior Vice President


                                          UCO COMPRESSION LLC


                                          By: /s/ Richard W. Fitzgerald
                                              ----------------------------------
                                                  Senior Vice President


                                          BRL UNIVERSAL COMPRESSION
                                          FUNDING I, L.P.

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


                                              By: /s/ Gregory C. Greene
                                                  ------------------------------
                                                      President


Signature Page - Amendment No. 3 to Management Agreement-Page 1
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                                     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
                                        ---------------------------------------
                                             Assistant Vice President


                                     Amendment No. 3 to the Management
                                     Agreement is hereby approved.

                                     FIRST UNION SECURITIES, INC., as deal
                                     agent


                                     By: /s/ Manoj Kumar
                                         --------------------------------------
                                              Vice President

                                     VARIABLE FUNDING CAPITAL
                                     CORPORATION, as note holder

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

                                         By: /s/ Manoj Kumar
                                             ----------------------------------
                                                  Vice President

Signature Page - Amendment No. 3 to Management Agreement-Page 2
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