Document:

<PAGE>   1
                                                                    EXHIBIT 10.3

                              AMENDMENT NUMBER ONE
                                     TO THE
                      UNIVERSAL COMPRESSION HOLDINGS, INC.
                           INCENTIVE STOCK OPTION PLAN

         WHEREAS, Universal Compression Holdings, Inc., a Delaware corporation
(the "Corporation"), previously adopted the Universal Compression Holdings, Inc.
Incentive Stock Option Plan (the "Plan");

         WHEREAS, Section 17 of the Plan reserves to the Corporation the right
to amend the Plan by action of its Board of Directors (the "Board"); and

         WHEREAS, the Corporation desires to amend the Plan in certain respects.

         NOW, THEREFORE, pursuant to the power of amendment reserved in Section
17 of the Plan, the Board amends the Plan as follows:

                                       1.

         Section 1 of the Plan is hereby amended, as of the date of adoption of
this Amendment, to add "and non-employee directors and consultants" after "key
executive employees" therein.

                                       2.

         The definition of the term "Participant" under Section 2 of the Plan is
hereby amended in its entirety, as of the date of adoption of this Amendment, to
provide as follows:

                  "Participant" means a key employee, non-employee director or
         consultant of the Corporation or a Subsidiary who is selected to
         participate in the Plan in accordance with Section 4.

                                       3.

         The definition of the term "Subsidiary" under Section 2 of the Plan is
hereby amended, as of the date of adoption of this Amendment, to add the
following new sentence to the end thereof:

         Notwithstanding the foregoing, for purposes of applying Section 422 of
         the Code to Options intended by the Administrator to be Incentive Stock
         Options, "Subsidiary" means a corporation that is a subsidiary
         corporation (within the meaning of Section 424(f) of the Code) of the
         Corporation.

                                       4.

         Section 4 of the Plan is hereby amended in its entirety, as of the date
of adoption of this Amendment, to provide as follows:

                  4. Participation. Participants in the Plan shall be limited to
         those key employees, non-employee directors and consultants of the
         Corporation and its Subsidiaries who have been notified in writing by
         the Administrator that they have been selected to participate in the
         Plan. Only Participants who are key employees of the

<PAGE>   2

Corporation or a Subsidiary shall be eligible for the grant of Incentive Stock
Options under the Plan.

                                       5.

         Sections 6 of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

                  6. Maximum Shares Available. The maximum aggregate number of
         shares available to be granted under the Plan is 257,572 shares of
         Common Stock, and such shares shall be reserved for Options granted
         under the Plan (subject to adjustment as provided in Section 10(h)).

                                       6.

         Section 10(h) of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

                  (h) Adjustments. The aggregate number and/or class of shares
         which may be available for the grant of Options and the number, class
         of and/or option price of shares subject to outstanding Options shall
         be adjusted by the Administrator to reflect a change in the
         capitalization of the Corporation resulting from a stock dividend or
         split, and may be adjusted by the Administrator to reflect a change in
         the capitalization of the Corporation resulting from a merger,
         consolidation, acquisition, separation (including a spin-off or
         spin-out), reorganization or liquidation; provided that the number of
         shares subject to any Option shall always be a whole number.
         Notwithstanding the foregoing, the issuance by the Corporation of
         shares of any class or securities convertible into shares of any class,
         for cash or property, or for labor or services, either upon direct sale
         or upon exercise of rights or warrants to subscribe therefor, or upon
         conversion of shares or obligations of the Corporation convertible into
         such shares or other securities, shall not affect, and no adjustment by
         reason thereof shall be made with respect to, the shares authorized for
         issuance under Section 4 or the shares subject to outstanding Options.

         IN WITNESS WHEREOF, the undersigned authorized officer of the
Corporation certifies that the Board adopted this Amendment Number One on April
20, 2000.

                                          /s/ Ernie L. Danner
                                          --------------------------------------
                                          Name: Ernie L. Danner
                                                --------------------------------
                                          Title: Executive Vice President
                                                --------------------------------<PAGE>   1
                                                                    EXHIBIT 10.4

                              AMENDMENT NUMBER TWO
                                     TO THE
                      UNIVERSAL COMPRESSION HOLDINGS, INC.
                           INCENTIVE STOCK OPTION PLAN

         WHEREAS, Universal Compression Holdings, Inc., a Delaware corporation
(the "Corporation"), previously adopted the Universal Compression Holdings, Inc.
Incentive Stock Option Plan (the "Plan");

         WHEREAS, Section 17 of the Plan reserves to the Corporation the right
to amend the Plan by action of its Board of Directors (the "Board"); and

         WHEREAS, the Corporation desires to amend the Plan in certain respects.

         NOW, THEREFORE, pursuant to the power of amendment reserved in Section
17 of the Plan, the Board amends the Plan as follows:

                                       1.

         Section 7 of the Plan is hereby amended, as of the date of adoption of
this Amendment, to add the following new sentence to the end thereof:

         No Participant in any calendar year shall be granted an Option to
         purchase more than 100,000 shares of Common Stock (subject to
         adjustment as provided in Section 10(h)).

                                       2.

         Section 10(c) of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

                  (c) Exercise of Option. Unless otherwise set forth in the
         written agreement evidencing the Option, each Option shall become
         exercisable in accordance with the following schedule:

                  Years from Grant Date                Amount Exercisable
                  ---------------------                ------------------
                       1 year                                33 1/3%
                       2 years                               33 1/3%
                       3 years                               33 1/3%

         Notwithstanding the foregoing, if the written agreement evidencing an
         Option so provides, the Option shall become immediately exercisable
         upon: (i) a public offering of Common Stock of the Corporation; (ii)
         the acquisition by any Person, other than an Affiliate of Castle Harlan
         Partners III, L.P., of fifty one percent (51%) or more of the Common
         Stock of the Corporation; or (iii) a sale of all or substantially all
         of the assets of the Corporation.

<PAGE>   2

                                       3.

         Section 10(d) of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

                  (d) Payment of Option Price Upon Exercise. The purchase price
         of the shares of Common Stock as to which an Option shall be exercised
         shall be paid to the Corporation at the time of exercise: (i) in cash;
         (ii) with the consent of the Board, by delivery of a promissory note to
         the Corporation payable over a three (3) year period and bearing
         interest at the prime rate; (iii) with the consent of the
         Administrator, by delivery of shares of Common Stock owned by the
         Participant having a Fair Market Value (as defined and determined by
         Section 2 hereof) equal in amount to the aggregate exercise price of
         the Option being exercised; (iv) by any combination of (i), (ii) and
         (iii); or (v) with the consent of the Administrator, by cancellation of
         a portion of the Option as determined by the Administrator.

                                       4.

         Section 10(e) of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

                  (e) Termination of Employment. Unless otherwise set forth in
         the written agreement evidencing the Option, (i) in the event the
         employment of a Participant terminates on account of death, Disability
         or retirement after age 65, (A) the Options that have been granted to
         such Participant and that are exercisable as of the date of the
         Participant's termination of employment may be exercised by such
         Participant, or his representative, within three (3) months after
         termination of employment and shall then terminate, and (B) the Options
         that have been granted to such Participant and that are not exercisable
         as of the date of the Participant's termination of employment shall
         terminate as of such date; (ii) in the event the employment of a
         Participant terminates for Cause, or a Participant voluntarily resigns
         his or her employment, the Options granted to such Participant, whether
         or not exercisable as of the date of the Participant's termination of
         employment, shall terminate on the date of termination; and (iii) in
         the event the employment of a Participant terminates for any reason
         other than death, Disability, retirement after age 65, Cause, or
         voluntary resignation, (A) the Options that have been granted to such
         Participant and that are exercisable as of the date of the
         Participant's termination of employment may be exercised by such
         Participant, or his representative, within thirty (30) days after
         termination of employment and shall then terminate, and (B) the Options
         that have been granted to such Participant and that are not exercisable
         as of the date of the Participant's termination of employment shall
         terminate as of such date.

                                      -2-
<PAGE>   3

                                       5.

         Section 10(h) of the Plan is hereby amended in its entirety, as of the
date of adoption of this Amendment, to provide as follows:

         The aggregate number and/or class of shares which may be available for
         the grant of Options, the annual grant cap described in Section 7, and
         the number, class of and/or option price of shares subject to
         outstanding Options shall be adjusted by the Administrator to reflect a
         change in the capitalization of the Corporation resulting from a stock
         dividend or split, and may be adjusted by the Administrator to reflect
         a change in the capitalization of the Corporation resulting from a
         merger, consolidation, acquisition, separation (including a spin-off or
         spin-out), reorganization or liquidation; provided that the number of
         shares subject to any Option shall always be a whole number.
         Notwithstanding the foregoing, the issuance by the Corporation of
         shares of any class or securities convertible into shares of any class,
         for cash or property, or for labor or services, either upon direct sale
         or upon exercise of rights or warrants to subscribe therefor, or upon
         conversion of shares or obligations of the Corporation convertible into
         such shares or other securities, shall not affect, and no adjustment by
         reason thereof shall be made with respect to, the shares authorized for
         issuance under Section 4 or the shares subject to outstanding Options.

                                       6.

         Section 10(k) of the Plan is hereby amended, as of the date of adoption
of this Amendment, to add the following new sentence to the end thereof:

         In addition, in the event the Stockholders Agreement terminates,
         certificates representing the shares of Common Stock issued pursuant to
         the Option may be issued omitting that portion of the restrictive
         legend stating that such shares are subject to the Stockholders
         Agreement and the availability of a copy of such agreement.

         IN WITNESS WHEREOF, the undersigned authorized officer of the
Corporation certifies that the Board adopted this Amendment Number Two on May
15, 2000.

                                          /s/ Ernie L. Danner
                                          --------------------------------------
                                          Name: Ernie L. Danner
                                                --------------------------------
                                          Title: Executive Vice President
                                                --------------------------------

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00010-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00010-of-00352.parquet"}]]