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                                                                     EXHIBIT 4.4

                               AMENDMENT NO. 5 TO
                              AMENDED AND RESTATED
                                RIGHTS AGREEMENT

         This Amendment No. 5 to Amended and Restated Rights Agreement (this
"Amendment") is entered into this 9th day of May, 2001 and shall become
effective upon the effectiveness of the Merger (as defined below). This
Amendment is an amendment to the Amended and Restated Rights Agreement, dated as
of March 17, 1989, as amended June 13, 1992, as amended and restated as of
December 12, 1997, as further amended November 24, 1998, March 10, 1999, May 19,
1999, and May 19, 2000 (the "Rights Agreement"), between Ocean Energy, Inc., a
Texas corporation (formerly known as Seagull Energy Corporation and referred to
herein as the "Company"), and Fleet National Bank (f/k/a BankBoston, N.A.) (the
"Rights Agent").

                                    RECITALS

         WHEREAS, the Company intends to merge (the "Merger") with and into its
wholly-owned subsidiary, Ocean Energy, Inc., a Delaware corporation
("OEI-Delaware), resulting in a redomestication of the Company from Texas to
Delaware;

         WHEREAS, in connection with the Merger, the Company desires to amend
the Rights Agreement to extend the Final Expiration Date (as defined therein)
for a period of two years;

         WHEREAS, in connection with the Merger, the common stock of the Company
and the preferred share purchase rights attached thereto will convert into
shares of common stock of OEI-Delaware having substantially identical preferred
share purchase rights attached thereto;

         WHEREAS, in connection with the Merger, OEI-Delaware desires to assume
the rights and obligations of the Company under the Rights Agreement; and

         WHEREAS, in furtherance of the foregoing and pursuant to and in
compliance with Section 26 of the Rights Agreement, the Company and the Rights
Agent wish to amend the Rights Agreement as set forth herein;

         NOW THEREFORE, the parties hereto agree as follows:

         Section 1. Amendments. Section 7(a) of the Rights Agreement is hereby
amended to provide that the term "Final Expiration Date" shall mean May 21,
2003.

         Section 2. Governing Law. Section 30 of the Rights Agreement is hereby
amended and restated to provide as follows:

         "This Agreement and each Right Certificate (and, prior to the
         Distribution Date, the Rights represented by certificates for Common
         Shares) issued hereunder shall be deemed to be a contract made under
         the laws of the State of Delaware and for all purposes shall be
         governed by and construed in accordance with the laws of



<PAGE>   2


         such State applicable to contracts to be made and performed entirely
         within such State."

         Section 3. Assumption by OEI-Delaware. Upon the effectiveness of the
Merger, OEI-Delaware hereby agrees to assume and to perform or discharge, in
accordance with their terms, all obligations of the Company under the Rights
Agreement and the Rights issued thereunder. The Rights Agent hereby consents to
the assumption by OEI-Delaware of the Company's rights and obligations under the
Rights Agreement and hereby agrees that all covenants and provisions thereunder
for the benefit of the Company shall inure to the benefit of OEI-Delaware.

         In furtherance of the foregoing, upon effectiveness of the Merger,
OEI-Delaware shall be substituted for the Company in all respects under the
Rights Agreement, and the Rights Agreement shall be amended as follows:

                  (a) Except where the context indicates otherwise, all
         references to the "Company" or to Seagull Energy Corporation shall be
         deemed to refer to Ocean Energy, Inc., a Delaware corporation;

                  (b) All references to Preferred Shares or Series B Junior
         Participating Preferred Stock shall be deemed to refer to the Series A
         Junior Participating Preferred Stock of OEI-Delaware, having the rights
         and preferences set forth in the Certificate of Designations set forth
         on Exhibit A to this Amendment, which replaces Exhibit A to the Rights
         Agreement;

                  (c) As provided in the Agreement and Plan of Merger relating
         to the Merger, all Rights outstanding and attached to the Common Shares
         at the effective time of the Merger shall by operation of the Merger be
         converted into Rights of OEI-Delaware having the same terms as the
         Rights immediately prior to the Merger, subject to the foregoing
         amendments;

                  (d) The Form of Rights Certificate attached as Exhibit B to
         the Rights Agreement, the Summary of Rights attached as Exhibit C to
         the Rights Agreement and other provisions of the Rights Agreement shall
         be deemed amended as appropriate to reflect the foregoing amendments.

         In addition, the parties hereby agree that the following sections shall
be amended as follows:

                  (a) The following language shall be inserted at the end of
         Section 2: ", upon ten (10) days' prior written notice to the Rights
         Agent. The Rights Agent shall have no duty to supervise, and shall in
         no event be liable for, the acts or omissions of any such co-Rights
         Agent";

                  (b) The address for notice for the Rights Agent in Section 25
         shall be revised as follows:

                  Fleet National Bank
                  c/o Equiserve Limited Partnership
                  150 Royall Street
                  Canton, MA 02021
                  Attn: Client Administration


                                       2
<PAGE>   3


                  (c) The word "negligence" in Sections 18 and 20(c) of the
         Rights Agreement shall be changed to "gross negligence."

         Section 4. Remainder of Agreement Not Affected. Except as set forth in
Sections 1, 2 and 3 hereof, the terms and provisions of the Rights Agreement
remain in full force and effect and are hereby ratified and confirmed.

         Section 5. Authority. Each party represents that such party has full
power and authority to enter into this Amendment, and that this Amendment
constitutes a legal, valid and binding obligation of such party, enforceable
against such party in accordance with its terms.

         Section 6. Counterparts. This Amendment may be executed in one or more
counterparts, each of which shall be deemed to be an original, but all of which
shall constitute one and the same agreement.



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<PAGE>   4



         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and attested, all as of the day and year first above written.



Attest:                                      OCEAN ENERGY, INC.,
                                             a Texas corporation


By: /s/ Robert K. Reeves                     By:  /s/ James T. Hackett
   ------------------------                     -----------------------------
        Robert K. Reeves                              James T. Hackett
        Executive Vice President, Senior              Chairman of the Board,
        General Counsel and Secretary                 President and
                                                      Chief Executive Officer

Attest:                                      OCEAN ENERGY, INC.,
                                             a Delaware corporation


By: /s/ Robert K. Reeves                     By:  /s/ James T. Hackett
   ------------------------                     -----------------------------
        Robert K. Reeves                              James T. Hackett
        Secretary                                     President


Attest:                                      FLEET NATIONAL BANK



By: /s/ Amy E. Toland                        By: /s/ Carol A. Mulvey-Eori
   ---------------------------------            -----------------------------
        Amy E. Toland                                Carol A. Mulvey-Eori
        Senior Account Manager                       Managing Director



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                                                                       EXHIBIT A

                 CERTIFICATE OF DESIGNATIONS OF PREFERRED SHARES




                                       5
<PAGE>   6



                           CERTIFICATE OF DESIGNATIONS
                                     FOR THE
                  SERIES A JUNIOR PARTICIPATING PREFERRED STOCK
                                       OF
                               OCEAN ENERGY, INC.


         OCEAN ENERGY, INC., a corporation duly organized and existing under the
laws of the State of Delaware (the "Company"), DOES HEREBY CERTIFY:

         That pursuant to authority conferred upon the Board of Directors of the
Company (the "Board") by the Certificate of Incorporation, as amended (the
"Certificate of Incorporation"), of the Company and pursuant to the provisions
of Section 151 of the General Corporation Law of the State of Delaware, the
Board duly adopted the following resolution on May 9, 2001.

         RESOLVED, that pursuant to the authority vested in the Board by the
provisions of the Certificate of Incorporation, the Board hereby creates the
Series A Junior Participating Preferred Stock (the "Series A Preferred Stock")
from the authorized but unissued preferred stock, par value $1.00 per share, of
the Company, and the Board hereby fixes the designations, powers, preferences
and relative, participating, optional and other special rights, and the
qualifications, limitations or restrictions thereof, of the shares of such
Series A Preferred Stock as follows:

         Section 1. Designation and Number. The shares of such series shall be
designated as "Series A Junior Participating Preferred Stock" and the number of
shares constituting the Series A Preferred Stock shall be 1,500,000. Such number
of shares may be increased or decreased by resolution of the Board; provided,
that no decrease shall reduce the number of shares of Series A Preferred Stock
to a number less than the number of shares then outstanding plus the number of
shares reserved for issuance upon the exercise of outstanding options, rights or
warrants or upon the conversion of any outstanding securities issued by the
Company convertible into Series A Preferred Stock.

         Section 2. Dividends and Distributions.

                  (A) Subject to the rights of the holders of any shares of any
         series of Preferred Stock (or any similar stock) ranking prior and
         superior to the Series A Preferred Stock with respect to dividends, the
         holders of shares of Series A Preferred Stock, in preference to the
         holders of Common Stock, par value $.10 per share (the "Common Stock"),
         of the Company, and of any other junior stock, shall be entitled to
         receive, when, as and if declared by the Board out of funds legally
         available for the purpose, quarterly dividends payable in cash on the
         last business day of March, June, September and December in each year
         (each such date being referred to herein as a "Quarterly Dividend
         Payment Date"), commencing on the first Quarterly Dividend Payment Date
         after the first issuance of a share or fraction of a share of Series A
         Preferred Stock, in an amount per share (rounded to the nearest cent)
         equal to the greater of (a) $1.00 or (b) subject to the provision for
         adjustment hereinafter set forth, 100 times the aggregate per share
         amount of all cash dividends, if any, and 100 times the aggregate per
         share amount (payable in kind) of all non-cash dividends or other
         distributions, if any, other than a dividend



<PAGE>   7


         payable in shares of Common Stock or a subdivision of the outstanding
         shares of Common Stock (by reclassification or otherwise), declared on
         the Common Stock since the immediately preceding Quarterly Dividend
         Payment Date or, with respect to the first Quarterly Dividend Payment
         Date, since the first issuance of any share or fraction of a share of
         Series A Preferred Stock. In the event the Company shall at any time
         declare or pay any dividend on the Common Stock payable in shares of
         Common Stock, or effect a subdivision or combination or consolidation
         of the outstanding shares of Common Stock (by reclassification or
         otherwise than by payment of a dividend in shares of Common Stock) into
         a greater or lesser number of shares of Common Stock, then in each such
         case the amount to which holders of shares of Series A Preferred Stock
         were entitled immediately prior to such event under clause (b) of the
         preceding sentence shall be adjusted by multiplying such amount by a
         fraction, the numerator of which is the number of shares of Common
         Stock outstanding immediately after such event and the denominator of
         which is the number of shares of Common Stock that were outstanding
         immediately prior to such event.

                  (B) The Company shall declare a dividend or distribution on
         the Series A Preferred Stock as provided in paragraph (A) of this
         Section immediately after it declares a dividend or distribution on the
         Common Stock (other than a dividend payable in shares of Common Stock);
         provided that, in the event no dividend or distribution shall have been
         declared on the Common Stock during the period between any Quarterly
         Dividend Payment Date and the next subsequent Quarterly Dividend
         Payment Date, a dividend of $1.00 per share on the Series A Preferred
         Stock shall nevertheless be payable on such subsequent Quarterly
         Dividend Payment Date.

                  (C) Dividends shall begin to accrue and be cumulative on
         outstanding shares of Series A Preferred Stock from the Quarterly
         Dividend Payment Date next preceding the date of issuance of such
         shares, unless the date of issuance of such shares is prior to the
         record date for the first Quarterly Dividend Payment Date, in which
         case dividends on such shares shall begin to accrue from the date of
         issuance of such shares, or unless the date of issuance is a Quarterly
         Dividend Payment Date or is a date after the record date for the
         determination of holders of shares of Series A Preferred Stock entitled
         to receive a quarterly dividend and before such Quarterly Dividend
         Payment Date, in either of which events such dividends shall begin to
         accrue and be cumulative from such Quarterly Dividend Payment Date.
         Accrued but unpaid dividends shall not bear interest. Dividends paid on
         the shares of Series A Preferred Stock in an amount less than the total
         amount of such dividends at the time accrued and payable on such shares
         shall be allocated pro rata on a share-by-share basis among all such
         shares at the time outstanding. The Board may fix a record date for the
         determination of holders of shares of Series A Preferred Stock entitled
         to receive payment of a dividend or distribution declared thereon,
         which record date shall be not more than 60 days prior to the date
         fixed for the payment thereof.

         Section 3. Voting Rights. The holders of shares of Series A Preferred
Stock shall have the following voting rights:

                  (A) Each share of Series A Preferred Stock shall entitle the
         holder thereof to 100 votes on all matters submitted to a vote of the
         shareholders of the Company.

<PAGE>   8


                  (B) Except as otherwise provided herein, in any other
         Statement of Resolution Establishing Series of Shares creating a series
         of Preferred Stock or any similar stock, or by law, the holders of
         shares of Series A Preferred Stock and the holders of shares of Common
         Stock and any other capital stock of the Company having general voting
         rights shall vote together as one class on all matters submitted to a
         vote of shareholders of the Company.

                  (C) Except as set forth herein or in the Certificate of
         Incorporation of the Company as in effect on the date hereof, or as
         otherwise provided by law, holders of Series A Preferred Stock shall
         have no special voting rights and their consent shall not be required
         (except to the extent they are entitled to vote with holders of Common
         Stock as set forth herein) for taking any corporate action.

         Section 4. Certain Restrictions.

                  (A) Whenever quarterly dividends or other dividends or
         distributions payable on the Series A Preferred Stock as provided in
         Section 2 are in arrears, thereafter and until all accrued and unpaid
         dividends and distributions, whether or not declared, on shares of
         Series A Preferred Stock outstanding shall have been paid in full, or
         declared and a sum sufficient for the payment therefor be set apart for
         payment and be in the process of payment, the Company shall not:

                  (i) declare or pay dividends, or make any other distributions,
                  on any shares of stock ranking junior (either as to dividends
                  or upon liquidation, dissolution or winding up) to the Series
                  A Preferred Stock;

                  (ii) declare or pay dividends, or make any other
                  distributions, on any shares of stock ranking on a parity
                  (either as to dividends or upon liquidation, dissolution or
                  winding up) with the Series A Preferred Stock, except
                  dividends paid ratably on the Series A Preferred Stock and all
                  such parity stock on which dividends are payable or in arrears
                  in proportion to the total amounts to which the holders of all
                  such shares are then entitled;

                  (iii) redeem or purchase or otherwise acquire for
                  consideration shares of any stock ranking junior (either as to
                  dividends or upon liquidation, dissolution or winding up) to
                  the Series A Preferred Stock, provided that the Company may at
                  any time redeem, purchase or otherwise acquire shares of any
                  such junior stock in exchange for shares of any stock of the
                  Company ranking junior (either as to dividends or upon
                  dissolution, liquidation or winding up) to the Series A
                  Preferred Stock; or

                  (iv) redeem or purchase or otherwise acquire for consideration
                  any shares of Series A Preferred Stock, or any shares of stock
                  ranking on a parity with the Series A Preferred Stock, except
                  in accordance with a purchase offer made in writing or by
                  publication (as determined by the Board) to all holders of
                  such shares upon such terms as the Board, after consideration
                  of the respective annual dividend rates and other relative
                  rights and preferences of the respective series


<PAGE>   9


                  and classes, shall determine in good faith will result in fair
                  and equitable treatment among the respective series or
                  classes.

                  (B) The Company shall not permit any subsidiary of the Company
         to purchase or otherwise acquire for consideration any shares of stock
         of the Company unless the Company could, under paragraph (A) of this
         Section 4, purchase or otherwise acquire such shares at such time and
         in such manner.

         Section 5. Reacquired Shares. Any shares of Series A Preferred Stock
purchased or otherwise acquired by the Company in any manner whatsoever shall be
retired and cancelled promptly after the acquisition thereof. All such shares
shall upon their cancellation become authorized but unissued shares of Preferred
Stock and may be reissued as part of a new series of Preferred Stock subject to
the conditions and restrictions on issuance set forth herein, in the Certificate
of Incorporation, or in any other Statement of Resolution Establishing Series of
Shares creating a series of Preferred Stock or any similar stock or as otherwise
required by law.

         Section 6. Liquidation, Dissolution or Winding Up. Upon any
liquidation, dissolution or winding up of the Company, no distribution shall be
made (1) to the holders of shares of stock ranking junior (either as to
dividends or upon liquidation, dissolution or winding up) to the Series A
Preferred Stock unless, prior thereto, the holders of shares of Series A
Preferred Stock shall have received $100 per share, plus an amount equal to
accrued and unpaid dividends and distributions thereon, whether or not declared,
to the date of such payment, provided that the holders of shares of Series A
Preferred Stock shall be entitled to receive an aggregate amount per share,
subject to the provision for adjustment hereinafter set forth, equal to 100
times the aggregate amount, if any, to be distributed per share to holders of
shares of Common Stock, or (2) to the holders of shares of stock ranking on a
parity (either as to dividends or upon liquidation, dissolution or winding up)
with the Series A Preferred Stock, except distributions made ratably on the
Series A Preferred Stock and all such parity stock in proportion to the total
amounts to which the holders of all such shares are entitled upon such
liquidation, dissolution or winding up. In the event the Company shall at any
time declare or pay any dividend on the Common Stock payable in shares of Common
Stock, or effect a subdivision or combination or consolidation of the
outstanding shares of Common Stock (by reclassification or otherwise than by
payment of a dividend in shares of Common Stock) into a greater or lesser number
of shares of Common Stock, then in each such case the aggregate amount to which
holders of shares of Series A Preferred Stock were entitled immediately prior to
such event under the proviso in clause (1) of the preceding sentence shall be
adjusted by multiplying such amount by a fraction, the numerator of which is the
number of shares of Common Stock outstanding immediately after such event and
the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

         Section 7. Consolidation, Merger, etc. In case the Company shall enter
into any consolidation, merger, combination or other transaction in which the
shares of Common Stock are exchanged for or changed into other stock or
securities, cash and/or any other property, then in any such case each share of
Series A Preferred Stock shall at the same time be similarly exchanged or
changed into an amount per share, subject to the provision for adjustment
hereinafter set forth, equal to 100 times the aggregate amount of stock,
securities, cash and/or any other property (payable in kind), as the case may
be, into which or for which each share of

<PAGE>   10


Common Stock is changed or exchanged. In the event the Company shall at any time
declare or pay any dividend on the Common Stock payable in shares of Common
Stock, or effect a subdivision or combination or consolidation of the
outstanding shares of Common Stock (by reclassification or otherwise than by
payment of a dividend in shares of Common Stock) into a greater or lesser number
of shares of Common Stock, then in each such case the amount set forth in the
preceding sentence with respect to the exchange or change of shares of Series A
Preferred Stock shall be adjusted by multiplying such amount by a fraction, the
numerator of which is the number of shares of Common Stock outstanding
immediately after such event and the denominator of which is the number of
shares of Common Stock that were outstanding immediately prior to such event.

         Section 8. No Redemption. The shares of Series A Preferred Stock shall
not be redeemable.

         Section 9. Rank. The Series A Preferred Stock shall rank, with respect
to the payment of dividends and the distribution of assets, on liquidation or
otherwise, junior to all series of any class of the Company's Preferred Stock.

         Section 10. Amendment. The Certificate of Incorporation and Bylaws of
the Company, and this Certificate of Designations, shall not be amended in any
manner that would materially alter or change the powers, preferences, privileges
or special rights of the Series A Preferred Stock so as to affect them adversely
without the affirmative vote of the holders of at least two-thirds of the
outstanding shares of Series A Preferred Stock, voting together as a single
class.