Document:

<PAGE>   1
                                    FORM OF
                          REGISTRATION RIGHTS AGREEMENT
                             INSTRUMENT OF ACCESSION

         In connection with [VALERIE L. BANNER ("BANNER")] [RICHARD W.
FITZGERALD ("Fitzgerald")], as a condition precedent to becoming the owner or
holder of record of FORTY (40) shares of Common Stock, par value $0.01 per
share, of Universal Compression Holdings, Inc., a Delaware corporation
("Holdings"), and ONE HUNDRED SIXTY (160) shares of Preferred Stock, par value
$0.01 per share, of Holdings, Holdings and [Banner] [Fitzgerald] hereby agrees
to become a stockholder, party to and bound by that certain Registration Rights
Agreement, dated as of February 20, 1998, by and among Holdings and certain
stockholders of Holdings. This Instrument of Accession shall take effect and
shall become an integral part of the said Registration Rights Agreement
immediately upon execution and delivery to Holdings of this Instrument.

         IN WITNESS WHEREOF, this INSTRUMENT OF ACCESSION has been duly executed
by or on behalf of the undersigned as of the date below written.

                                  Signature:
                                             ----------------------------------
                                  Address
                                  For Notice:
                                             ----------------------------------

                                             ----------------------------------

                                             ----------------------------------

                                  Date:
                                        ---------------------------------------

                                  UNIVERSAL COMPRESSION HOLDINGS, INC.

                                  By:
                                        ---------------------------------------

                                  Name:
                                        ---------------------------------------

                                  Date:
                                        ---------------------------------------<PAGE>   1
                                    FORM OF
                             STOCKHOLDERS AGREEMENT
                             INSTRUMENT OF ACCESSION

         The undersigned, [VALERIE L. BANNER] [RICHARD W. FITZGERALD], as a
condition precedent to becoming the owner or holder of record of FORTY (40)
shares of Common Stock, par value $0.01 per share, of Universal Compression
Holdings, Inc., a Delaware corporation ("Holdings"), and ONE HUNDRED SIXTY (160)
shares of Preferred Stock, par value $0.01 per share, of Holdings, hereby agrees
to become a stockholder, party to and bound by that certain Stockholders
Agreement, dated as of February 20, 1998, by and among Holdings and certain
stockholders of Holdings. This Instrument of Accession shall take effect and
shall become an integral part of the said Stockholders Agreement immediately
upon execution and delivery to Holdings of this Instrument.

         IN WITNESS WHEREOF, this INSTRUMENT OF ACCESSION has been duly executed
by or on behalf of the undersigned as of the date below written.

                                    Signature:
                                               -------------------------------

                                    Address

                                    For Notice:
                                               -------------------------------

                                               -------------------------------

                                               -------------------------------

                                         Date:
                                               -------------------------------

Accepted:

UNIVERSAL COMPRESSION HOLDINGS, INC.

By:
    -----------------------------------

Date:
      ---------------------------------<PAGE>   1

                                    FORM OF
                       MANAGEMENT STOCK BUYBACK AGREEMENT

                  STOCK BUYBACK AGREEMENT, dated as of January 31, 2000 (the
"Agreement"), by and among UNIVERSAL COMPRESSION HOLDINGS, INC., a Delaware
corporation ("Holdings") and [RICHARD W. FITZGERALD] [VALERIE L. BANNER]
("Purchaser").

                  WHEREAS, Holdings and the Purchaser are parties to the
Subscription Agreement, dated the date hereof (the "Subscription Agreement"),
whereby Purchaser is acquiring the number of shares of the Common Stock of
Holdings, par value $0.01 per share (the "Common Stock"), and the number of
shares of the Series A Preferred Stock of Holdings, par value $.01 per share
(the "Preferred Stock") as is set forth opposite such person's name on Annex I;

                  WHEREAS, in connection with such purchase, Holdings and the
Purchaser wish to set forth their understanding with respect to their respective
rights to force the sale, in the case of Holdings, or force the purchase, in the
case of the Purchaser, of the Common Stock and/or Preferred Stock acquired
pursuant to the Subscription Agreement.

                  NOW, THEREFORE, the parties hereto agree as follows:

                  1. General. Except as provided in Sections 3, 4, 5 and 7 of
the Stockholders Agreement, dated as of February 20, 1998, by and among Holdings
and the stockholders party thereto (the "Stockholders Agreement"), each share of
Common Stock and Preferred Stock acquired by the Purchaser at any time may not
be sold, disposed of or otherwise transferred except to Holdings in accordance
with this Agreement. Each certificate representing shares of Common Stock and
Preferred Stock acquired by Purchaser shall bear a legend to such effect. In the
event that Purchaser, in accordance with the Stockholders Agreement, transfers
all or any shares of Common Stock or Preferred Stock to a person other than
Holdings, such transferee shall be obligated to comply with the provisions of
this Agreement. The Common Stock and Preferred Stock are sometimes collectively
referred to herein as the "Holdings Securities."

                  2. Call by Holdings. Within six months following Purchaser's
termination of employment with Holdings and Universal Compression, Inc.,
Holdings shall have the right to purchase from Purchaser, all of the Holdings
Securities owned by Purchaser for an amount equal to:

                  (a) in the case of Common Stock (i) where Purchaser resigns
prior to the expiration (the "Expiration") of Purchaser's term of employment
under Purchaser's employment agreement, if any, or is terminated for Cause at
any time, the lesser of (x) the product of (A) the Common Share Value (valued as
of the end of the month preceding Purchaser's resignation from or termination of
employment) multiplied by (B) the number of shares of Common Stock held by
Purchaser, and (y) the product of (A) the price per share of Common Stock paid
by Purchaser to acquire such shares multiplied by (B) the number of shares of
Common Stock held by Purchaser, or (ii) where Purchaser resigns after the
Expiration, the Fair Market Value of such shares of Common Stock, and

                  (b) in the case of Preferred Stock (i) where Purchaser resigns
prior to the Expiration or is terminated for Cause at any time, the product of
(A) the Preferred Share Value multiplied by (B) the number of shares of
Preferred Stock held by Purchaser, or (ii) where Purchaser resigns after the
Expiration, the Fair Market Value of such shares of Preferred Stock.

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Management Stock Buyback Agreement                                        1 of 6
Universal Compression Holdings, Inc.
<PAGE>   2

                  If such purchase of Holdings Securities by Holdings is
prohibited pursuant to the terms of any agreement to which Holdings is a party,
the period during which Holdings may make such purchase shall be extended by an
additional six months from the expiration of the initial six-month period.

                  3. Put by Purchaser. Purchaser shall have the right to sell to
Holdings, within three months following Purchaser's death or disability or
termination of employment by Holdings for any reason other than Cause, all of
the Holdings Securities owned by Purchaser for an amount equal to:

                  (a) in the case of Common Stock, the Fair Market Value of such
shares of Common Stock, and

                  (b) in the case of Preferred Stock, the Fair Market Value of
such shares of Preferred Stock.

                  4. Definitions. For purposes of this Agreement:

                  (i) "Cause" shall mean termination (a) upon the willful and
continued failure by Purchaser to substantially perform his duties with Holdings
or its subsidiaries (other than any such failure resulting from his incapacity
due to physical or mental illness), after a written demand for substantial
performance is delivered to Purchaser by the Board of Directors of Holdings or
such subsidiary, which demand specifically identifies the manner in which
Purchaser is believed not to have substantially performed his duties, or (b)
Purchaser's willful engagement in conduct which is or is likely to become
demonstrably and materially injurious to Holdings or such subsidiary, monetarily
or otherwise;

                  (ii) "Common Share Value" shall mean the quotient of (i) the
amount equal to the excess, if any, of the Holdings Equity Value over the
Holdings Preferred Value divided by (ii) the number of shares of Common Stock
outstanding on a fully diluted basis.

                  (iii) "EBITDA" shall mean, for any period, the amount equal
to: (a) the net income (or net loss) of Holdings and its subsidiaries during
such period after deduction of all expenses, taxes and other charges, determined
in accordance with generally accepted accounting principles, after eliminating
therefrom all extraordinary items of income and expense (including the
elimination of any expense reported on the financial statements of Holdings or
any subsidiary for such period in respect of the management fee owed to Castle
Harlan, Inc. ("CHI") pursuant to the Management Agreement between CHI, Holdings
and Universal Compression, Inc., dated as of the date hereof); plus (b) to the
extent deducted from net income, dividends on Holdings' Preferred Stock; plus
(c) any provision for (or less any benefit from) income taxes included in the
determination of (a) above; plus (d) depreciation, depletion and amortization;
plus (e) the expenses of Holdings and its subsidiaries charged to income for
interest on indebtedness (including the current portion thereof), determined in
accordance with generally accepted accounting principles.

                  (iv) "Fair Market Value" shall mean the fair market value of
the shares of Common Stock or Preferred Stock, as the case may be, that are
being purchased from or sold by a Purchaser pursuant to this Agreement, such
value to be determined by a nationally recognized investment banking firm
selected by the Board of Directors of Holdings, which selection shall be

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Management Stock Buyback Agreement                                        2 of 6
Universal Compression Holdings, Inc.
<PAGE>   3

subject to Purchaser's approval (such approval or disapproval not to be
unreasonably withheld) within thirty (30) days of notice to him of such
selection.

                  (v) "Holdings Equity Value" shall mean, as of any date, an
amount equal to EBITDA for the four immediately preceding fiscal quarters,
multiplied by seven, minus the sum of (a) the amount of Holdings' indebtedness
for borrowed money (including any obligation owed in respect of capitalized
leases) (determined in accordance with generally accepted accounting principles
as set forth on Holdings' most recent quarterly balance sheet, including current
and long term portions) and accrued interest thereon, and (b) the amount of the
liquidation preference of any preferred stock (other than Preferred Stock)
outstanding and accrued dividends thereon.

                  (vi) "Holdings Preferred Value" shall mean the Preferred Share
Value multiplied by the number of shares of Preferred Stock outstanding on a
fully diluted basis.

                  (vii) "Preferred Share Value" shall mean the lesser of (a) the
Holdings Equity Value divided by the number of shares of Preferred Stock
outstanding on a fully diluted basis and (b) the liquidation value per share of
Preferred Stock assigned to the Preferred Stock, plus all accrued and unpaid
dividends thereon, if any.

                  5. Payment. The purchase of Holdings Securities by Holdings
pursuant to the foregoing provisions shall be paid for in cash, to the extent
permitted under the loan agreements and debt instruments relating to Holdings or
any of its subsidiaries, or, to the extent cash payments are not permitted
thereunder, by means of a subordinated payment-in-kind promissory note issued by
Holdings bearing interest, payable annually, at the lowest interest rate
required to avoid imputed interest, which note shall be repaid as soon as
permitted.

                  6. Further Action. Each party hereto agrees to execute and
deliver any instrument and take any action that may reasonably be requested by
any other party for the purpose of effectuating the provisions of this
Agreement.

                  7. Miscellaneous Provisions.

                     (a) Assignability; Binding Effect. Except as otherwise
provided in this Section, no right under this Agreement shall be assignable and
any attempted assignment in violation of this provision shall be void. Holdings
shall have the right to assign its rights and obligations hereunder to any
successor entity (including any entity acquiring substantially all of the assets
of Holdings), whereupon references herein to Holdings shall be deemed to be to
such successor. This Agreement, and the rights and obligations of the parties
hereunder, shall be binding upon and inure to the benefit of any and all
successors, permitted assigns, personal representatives and all other legal
representatives, in whatsoever capacity, by operation of law or otherwise, of
the parties hereto, in each case with the same force and effect as if the
foregoing persons were named herein as parties hereto.

                     (b) Notices. Any notice or other communication required or
which may be given hereunder shall be in writing and shall be delivered
personally, telecopied with confirmed receipt, sent by certified, registered, or
express mail, postage prepaid, or sent by a national next-day delivery service
to the parties at the following addresses or at such other addresses as shall be
specified by the parties by like notice, and shall be deemed given when so

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Management Stock Buyback Agreement                                        3 of 6
Universal Compression Holdings, Inc.

<PAGE>   4

delivered personally or telecopied, or if mailed, 2 days after the date of
mailing, or, if by national next-day delivery service, on the day after delivery
to such service as follows:

                                    (i)     if to Holdings, to it at:

                                            c/o Castle Harlan, Inc.
                                            150 East 58th Street, 37th Floor
                                            New York, New York  10155
                                            Attention:  Jeffrey M. Siegal
                                            Telecopier No.:  212-207-8042

                                    with a copy to:

                                            Schulte Roth & Zabel LLP
                                            900 Third Avenue
                                            New York, New York 10022
                                            Attention:  Andre Weiss, Esq.

                                    (ii)    if to Purchaser, to him or her at:

                                            Universal Compression, Inc.
                                            4440 Brittmoore Road
                                            Houston, Texas  77041-8004

                     (c) Applicable Law; Consent to Jurisdiction. This Agreement
and the validity and performance of the terms hereof shall be governed by and
construed in accordance with the laws of the State of New York without regard to
principles of conflicts of law or choice of law. The parties hereto hereby agree
that all actions or proceedings arising directly or indirectly from or in
connection with this Agreement shall be litigated only in the Supreme Court of
the State of New York or the United States District Court for the Southern
District of New York located in New York County, New York. To the extent
permitted by applicable law, the parties hereto consent to the jurisdiction and
venue of the foregoing courts and consent that any process or notice of motion
or other application to either of said courts or a judge thereof may be served
inside or outside the State of New York or the Southern District of New York by
registered mail, return receipt requested, directed to such party at its address
set forth in this Agreement (and service so made shall be deemed complete five
days after the same has been posted as aforesaid) or by personal service or in
such other manner as may be permissible under the rules of said courts.

                     (d) Entire Agreement; Amendments and Waivers. This
Agreement sets forth the entire understanding of the parties with respect to the
subject matter hereof. The failure of any party to seek redress for the
violation of or to insist upon the strict performance of any term of this
Agreement shall not constitute a waiver of such term and such party shall be
entitled to enforce such term without regard to such forbearance. This Agreement
may be amended only by the written consent of each party hereto, and each party
hereto may take any action herein prohibited or omit to take action herein
required to be performed by it, and any breach of or compliance with any
covenant, agreement, warranty or representation may be waived only by the
written waiver of the party against whom such action or inaction may negatively
affect, but, in any case, such consent or waiver shall only be effective in the
specific instance and for the specific purpose for which given.

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Management Stock Buyback Agreement                                        4 of 6
Universal Compression Holdings, Inc.

<PAGE>   5

                     (e) Headings. The headings in this Agreement are for
reference purposes only and shall not in any way affect the meaning or
interpretations of the Agreement.

                     (f) Severability. If any term, provision, covenant or
restriction of this Agreement, or any part thereof, is held by a court of
competent jurisdiction or any foreign federal, state, county or local government
or any other governmental, regulatory or administrative agency or authority to
be invalid, void, unenforceable or against public policy for any reason, the
remainder of the terms, provisions, covenants and restrictions of this Agreement
shall remain in full force and effect and shall in no way be affected, impaired
or invalidated.

                     (g) Counterparts. This Agreement may be executed in two or
more counterparts, each of which shall be deemed an original, but all of which
shall constitute one and the same instrument, and it shall not be necessary in
making proof of this Agreement to produce or account for more than one such
counterpart.

                     (h) Specific Performance. Each of the parties hereto
acknowledges and agrees that in the event of any breach of this Agreement, the
non-breaching party would be irreparably harmed and could not be made whole by
monetary damages. It is accordingly agreed that the parties hereto shall and do
hereby waive the defense in any action for specific performance that a remedy at
law would be adequate and that the parties hereto, in addition to any other
remedy to which they may be entitled at law or in equity, shall be entitled to
compel specific performance of this Agreement in any action instituted in the
Supreme Court of the State of New York or the United States District Court for
the Southern District of New York, or, in the event such courts shall not have
jurisdiction of such action, in any court of the United States or any state
thereof having subject matter jurisdiction of such action.

                  IN WITNESS WHEREOF, the undersigned have executed this
Agreement as of the date first set forth above.

                                      UNIVERSAL COMPRESSION HOLDINGS, INC.

                                      By:
                                         ---------------------------------------

                                      Name:
                                           -------------------------------------

                                      Title:
                                            ------------------------------------

                                      PURCHASER:

                                      ------------------------------------------

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Management Stock Buyback Agreement                                        5 of 6
Universal Compression Holdings, Inc.
<PAGE>   6

                                     ANNEX I

<TABLE>
<CAPTION>
           PURCHASER                  NUMBER OF SHARES                     PURCHASE PRICE
           ---------                  ----------------                     --------------
                                COMMON                PREFERRED      COMMON              PREFERRED
                                STOCK                   STOCK        STOCK                 STOCK
                                -----                   -----        -----                 -----
<S>                             <C>                   <C>           <C>                  <C>

</TABLE>

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Management Stock Buyback Agreement                                        6 of 6
Universal Compression Holdings, Inc.

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