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                                                                     EXHIBIT 4.1

                          CERTIFICATE OF DESIGNATIONS


                                    FOR THE


                     SERIES A CONVERTIBLE 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 November 4, 1998:

  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
Convertible Preferred Stock (the "Series A Preferred Stock") from the authorized
but unissued preferred stock, par value $.01 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 I.  Designation and Number.  A series of fifty thousand (50,000)
shares shall be designated the Series A Convertible Preferred Stock.  The number
of shares in such series may be increased or decreased (but not below the number
of shares then outstanding) from time to time by the Board.

  Section II.  Definitions.


  A. For purposes of this resolution, the following terms shall have the
     meanings indicated:

  The term "Available Cash" still have the meaning given to it in Section VII.C.

  The term "Capital Stock" shall mean any and all shares or other equivalents
(however designated) of corporate stock of the Company or the entity in
question, as the case may be.



  The term "Closing Date" shall mean November 10, 1998.
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  The term "Common Stock" shall mean the Company's Common Stock, par value $.01
per share.


  The term "Conversion Price" shall mean the Series A Conversion Price.

  The term "Current Market Price" shall mean, as of any date, the price per
share of Common Stock determined by the Company's Board as provided in this
definition. The Current Market Price shall be the average of the daily closing
prices per share of Common Stock for ten consecutive trading days ending no more
than two business days before the day in question (as adjusted for any stock
dividend, split, combination or reclassification that took effect during or
subsequent to such ten trading day period). The closing price for each day shall
be the last reported sales price regular way or, in the event no such reported
sales take place on such day, the average of the last reported bid and asked
prices regular way, in either case on the principal national securities exchange
on which the Common Stock is listed or admitted to trading, or if not listed or
admitted to trading on any national securities exchange, the average of the
highest bid and the lowest asked prices quoted on the National Association of
Securities Dealers Automated Quotation System; provided, however, that if the
Common Stock is not traded in such manner that such quotations are available for
the period required hereunder, the Current Market Price per share of Common
Stock shall be deemed to be the fair value as reasonably determined by the Board
of the Company. Notwithstanding the foregoing, to the extent the Company sells
Common Stock in a public offering, the Current Market Price with respect to such
transaction shall be the price per share at which the Company sells such Common
Stock before deducting therefrom any discounts, commissions, taxes or other
expenses allowed, paid or incurred by the Company for any underwriting or
otherwise in connection with the issuance and sale thereof.

  The term "Junior Securities" shall have the meaning given to it in Section
VIII.

  The term "Liquidation" shall mean any voluntary or involuntary liquidation,
dissolution or winding-up of the Company. Neither the sale, conveyance, exchange
or transfer (for cash, shares of stock, securities or other consideration) of
all or substantially all of the property or assets of the Company nor the
consolidation or merger of the Company with or into one or more entities shall
be deemed to be a liquidation, dissolution or winding-up of the Company.

  The term "Mandatorily Redeemable Preferred Stock" shall have the meaning given
to it in Section VII.C.

  The term "Parity Securities" shall have the meaning given to it in Section
VIII.

  The term "Optional Redemption Date" shall have the meaning given to it in
Section VII.B.

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  The term "Optional Redemption Notice" shall have the meaning given to it in
Section VII.B.



  The term "Reclassification" means any capital reorganization of the Company,
any reclassification of the Common Stock, the consolidation of the Company with
or the merger of the Company with or into any other Person, or the sale, lease
or other transfer of all or substantially all of the assets of the Company to
any other Person. The subdivision or combination of shares of Common Stock
issuable upon conversion of shares of Series A Preferred Stock at any time
outstanding into a greater or lesser number of shares of Common Stock (whether
with or without par value) shall not be deemed to be a "Reclassification" of the
Common Stock for the purposes of Section VI.E.4.

  The term "Redemption Date" shall have the meaning given to it in Section
VII.C.

  The term "Rights" means the rights to acquire Capital Stock or preferred stock
of the Company, or subdivsions thereof, which are issued pursuant to that
certain Rights Agreement of the Company dated December 22, 1997, as amended, or
pursuant to any other rights plan approved by the Board and any amendments
thereto, similar to shareholder rights plans of the type adopted by public
companies, approval of any rights plan by the Board to be conclusive evidence
that such plan satisfies the foregoing and such rights issuable thereunder are
Rights contemplated hereby.

  The term "Senior Securities" shall have the meaning given to it in Section
VIII.

  The term "Series A Conversion Date" shall have the meaning set forth in
Section VI.D hereof.

  The term "Series A Conversion Price" shall have the meaning set forth in
Section VI.C hereof.

  The term "Series A Forced Conversion Price" means prior to the third
anniversary of the Closing Date, 175% of the Series A Conversion Price, as then
in effect, and on and after the third anniversary of the Closing Date, 150% of
the Series A Conversion Price, as then in effect.

  The term "Series A Preferred Stock" means the Series A Convertible Preferred
Stock, par value $.01 per share, of the Company.

  The term "Trigger Price" shall mean, as applicable, (i) in the case of Common
Stock, options, warrants or other rights to purchase or acquire Common Stock,
securities by their terms convertible into or exchangeable for Common Stock
(other than any series of convertible preferred stock) and Capital Stock, other
than any series of convertible preferred stock, of the Company, $12.00 per
share, as proportionately adjusted for all Common Stock stock splits, dividends
paid in Common Stock, reverse splits of Common Stock and other recapitalizations
affecting the Common Stock subsequent to the Closing Date or (ii) in the 

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case of any series of convertible preferred stock of the Company, the Series A
Conversion Price as then in effect.

        B. All accounting terms used herein and not expressly defined herein
     shall have the meanings given to them in accordance with generally accepted
     accounting principles as of the date the Series A Preferred Stock is
     initially issued.

  Section III.  Dividends.  The holders of the then outstanding Series A
Preferred Stock shall be entitled to receive, when and as declared by the Board,
and out of any funds legally available therefor, cumulative dividends at the
annual rate of $65.00 per share, payable semi-annually in cash on April 1 and
October 1 of each year commencing April 1, 1999.  Dividends on the Series A
Preferred Stock shall accumulate and accrue on each such share from the date of
its original issue and shall accrue from day to day thereafter, whether or not
earned or declared. No dividend or distribution on any Junior Securities in
cash, shares of stock (other than Common Stock) or other property shall be
declared, set apart for payment or paid unless all previous and current
dividends on the Series A Preferred Stock at the rate specified above shall have
been paid or declared and a sum sufficient for the payment thereof set apart.

  Section IV.  Preference on Liquidation. Upon any Liquidation, holders of
shares of Series A Preferred Stock shall be entitled to receive payment of
$1,000.00 per share of Series A Preferred Stock held by them plus an amount
equal to all accrued and unpaid dividends thereon, whether or not earned or
declared, to and including the last date on which dividends have accrued thereon
prior to the Liquidation, before any distribution shall be made or any assets
distributed to the holders of any of the Junior Securities.  Except as provided
in the preceding sentence, holders of Series A Preferred Stock shall not be
entitled to any distribution in the event of any Liquidation of the affairs of
the Company.  If the assets of the Company are not sufficient to pay in full the
liquidation payments payable to the holders of outstanding shares of the Series
A Preferred Stock and all Parity Securities, then the holders of all such shares
shall share equally and ratably in such distribution of assets in proportion to
the full liquidation preference to which each is entitled, including without
limitation, accumulated but unpaid dividends.


  Section V.  Voting.


        A. In addition to the special voting rights provided in paragraph "B" of
     this Section V and the voting rights provided by applicable law, the
     holders of shares of Series A Preferred Stock shall be entitled to vote
     upon all matters upon which holders of the Common Stock have the right to
     vote, and shall be entitled to the number of votes equal to the largest
     number of full shares of Common Stock into which such shares of Series A
     Preferred Stock could be converted pursuant to the provisions of Section VI
     hereof at the record date for the determination of the stockholders
     entitled to vote on such matters or, if no such record date is established,
     the date such vote is taken, such votes to be counted together with all
     other shares of Capital Stock having general voting powers and not
     separately as a class. In all cases where the holders of shares of Series A
     Preferred Stock have the right to vote separately as a class, all such
     holders shall be entitled to the number of votes equal to the largest
     number of full shares of Common Stock into which such shares of

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     Series A Preferred Stock could be converted pursuant to the provisions of
     Section VI hereof at the record date for the determination of the
     stockholders entitled to vote on such matters or, if no such record date is
     established, at the date such vote is taken.

        B. So long as any Series A Preferred Stock is outstanding, without the
     consent of the holders of at least 66 2/3% of the shares of Series A
     Preferred Stock then outstanding, voting together as a class, given in
     writing or by vote at a meeting of stockholders called for such purpose,
     the Company will not (i) create any new class or series of stock having a
     preference over the Series A Preferred Stock with respect to dividend
     distributions or distributions on Liquidation or (ii) amend, alter or
     repeal any provision of the Certificate of Incorporation of the Company so
     as to adversely affect the preferences, rights, or powers of the Series A
     Preferred Stock.

Section VI.  Conversion Rights.  The Series A Preferred Stock shall be
convertible into Common Stock as follows:

        A. Optional Conversion. Subject to and upon compliance with the
     provisions of this Section VI, the holder of any shares of Series A
     Preferred Stock shall have the right at such holder's option, at any time
     or from time to time, to convert any of such shares of Series A Preferred
     Stock into the number of fully paid and nonassessable shares of Common
     Stock set forth in paragraph "C" of this Section VI.

        B. Automatic Conversion. Each outstanding share of Series A Preferred
     Stock shall automatically be converted, without any further act of the
     Company or its stockholders, into the number of fully paid and
     nonassessable shares of Common Stock set forth in paragraph "C" of this
     Section VI, provided, however, that such automatic conversion shall occur
     if, and only if, for any 20 consecutive trading days, the closing price of
     the Common Stock equals or exceeds the Series A Forced Conversion Price.

        C. Conversion Price.  Each share of Series A Preferred Stock converted
     pursuant to paragraphs "A" and "B" of this Section VI shall be converted
     into such number of shares of Common Stock as is determined by dividing (i)
     the sum of (A) $1,000.00 plus (B) all accrued and unpaid dividends on such
     share of Series A Preferred Stock, whether or not earned or declared, which
     such holder is entitled to receive, but has not yet received, by (ii) the
     Series A Conversion Price in effect on the Series A Conversion Date.  The
     Series A Conversion Price shall initially be $15.00.  The Series A
     Conversion Price shall be subject to adjustment as set forth in paragraph
     "E" of this Section VI and as so adjusted is referred to herein as the
     "Series A Conversion Price."

        D. Mechanics of Conversion. Upon the occurrence of the event specified
     in paragraph "B" of this Section VI, the outstanding shares of Series A
     Preferred Stock shall be converted automatically without any further action
     by the holders of such shares and regardless of whether the certificates
     representing such shares are surrendered to the Company or its transfer
     agent; provided, however, that the Company shall not be obligated to issue
     to any such holder certificates evidencing the shares of Common Stock
     issuable 

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     upon such conversion unless certificates evidencing such shares of Series A
     Preferred Stock are delivered to either the Company or any transfer agent
     of the Company or the affidavit and indemnity referenced in paragraph "F"
     of Section IX hereof with respect to such certificates are delivered to the
     Company. The holder of any shares of Series A Preferred Stock may exercise
     the conversion right specified in paragraph "A" of this Section VI as to
     any part thereof by surrendering to the Company or any transfer agent of
     the Company the certificate or certificates for the shares to be converted,
     accompanied by written notice stating that the holder elects to convert all
     or a specified portion of the shares represented thereby. Conversion shall
     be considered to have been effected (i) on the date of the occurrence of
     the event specified in paragraph "B" of this Section VI, or (ii) on the
     date when a holder of Series A Preferred Stock delivers notice of an
     election to convert shares of Series A Preferred Stock to the Company
     accompanied by certificates representing such shares, as the case may be,
     and such date is referred to herein as the "Series A Conversion Date."
     Subject to the provisions of paragraph "E" of this Section VI, as promptly
     as practicable thereafter (and after surrender of the certificate or
     certificates representing shares of the Series A Preferred Stock to the
     Company or any transfer agent of the Company or delivery to the Company of
     the affidavit and indemnity referenced in paragraph "F" of Section IX
     hereof with respect to such certificates), the Company shall issue and
     deliver to or upon the written order of such holder a certificate or
     certificates for the number of full shares of Common Stock to which such
     holder is entitled and a check in immediately available funds or cash with
     respect to any fractional interest in a share of Common Stock as provided
     in paragraph "C" of Section IX hereof. Subject to the provisions of
     paragraph "E" of this Section VI, the person in whose name the certificate
     or certificates for Common Stock are to be issued shall be considered to
     have become a holder of record of such Common Stock on the Series A
     Conversion Date. Upon conversion of only a portion of the number of shares
     covered by a certificate representing shares of Series A Preferred Stock
     surrendered for conversion, the Company shall issue and deliver to or upon
     the written order of the holder of the certificate so surrendered for
     conversion, at the expense of the Company, a new certificate or
     certificates covering the number of shares of Series A Preferred Stock
     representing the unconverted portion of the certificate so surrendered.

        E. Series A Conversion Price Adjustments. The Series A Conversion Price
     shall be subject to adjustment from time to time as follows:

             1. Other Issuances of Common Stock. If the Company shall issue any
          Additional Shares of Common Stock after the Closing Date for a
          consideration per share less than the Trigger Price immediately prior
          to such issuance, then and in each such case the Series A Conversion
          Price shall immediately be reduced to a price determined by
          multiplying the Series A Conversion Price by a fraction (i) the
          numerator of which shall be (A) the number of shares of Common Stock
          outstanding at the close of business on the day next preceding the
          date of such issue, plus (B) the number of shares of Common Stock
          which the aggregate consideration received (or by the express
          provisions hereof deemed to have been received) by the Company for the
          total number of Additional Shares of Common Stock so issued would
          purchase at such Trigger Price and (ii) the denominator of which shall
          be the

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          number of shares of Common Stock outstanding at the close of
          business on the date of such issue after giving effect to such issue
          of Additional Shares of Common Stock.  For the purpose of the
          calculation described in this clause "1", the number of shares of
          Common Stock outstanding shall include (A) the number of shares of
          Common Stock into which the then outstanding shares of Series A
          Preferred Stock could be fully converted on the day next preceding the
          issue of Additional Shares of Common Stock and (B) the number of
          shares of Common Stock which could be obtained through the conversion
          of all convertible securities which are convertible on the day next
          preceding the issue of Additional Shares of Common Stock.  "Additional
          Shares of Common Stock" shall mean all shares of Common Stock issued
          by the Company after the Closing Date, whether or not subsequently
          reacquired or retired by the Company, other than (i) shares of Common
          Stock issued upon conversion of the Series A Preferred Stock and (ii)
          shares of Common Stock issued to, and options or rights to purchase
          Common Stock granted to, current or former management, directors, or
          employees of, or consultants to the Company or any subsidiary of the
          Company pursuant to stock purchase or stock option plans or other
          arrangements that are approved by the Board or the Compensation
          Committee of the Board.  For the purpose of any adjustment of the
          Series A Conversion Price pursuant to this clause "1", the following
          provisions shall be applicable:

                    a.  Cash.  In the case of the issuance of Common Stock for
               cash, the amount of the consideration received by the Company
               shall be considered to be the amount of the cash proceeds
               received by the Company for such Common Stock before deducting
               therefrom any discounts, commissions, taxes or other expenses
               allowed, paid or incurred by the Company for any underwriting or
               otherwise in connection with the issuance and sale thereof.

                    b.  Consideration Other Than Cash.  In the case of the
               issuance of Common Stock (otherwise than upon the conversion of
               shares of capital stock or other securities of the Company) for a
               consideration in whole or in part other than cash, including
               securities acquired in exchange therefor (other than securities
               by their terms so exchangeable), the consideration other than
               cash shall be deemed to be the fair value thereof as reasonably
               determined by the Board, irrespective of any accounting
               treatment; provided, however, that such fair value as reasonable
               determined by the Board shall not exceed the aggregate Current
               Market Price of the shares of Common Stock being issued as of the
               date the Board authorizes the issuance of such shares.

                    c.  Options and Convertible Securities.  If, after the
               Closing Date, the Company shall grant any options, warrants or
               other rights to purchase or acquire Common Stock (whether or not
               at the time exercisable), or issue any securities by their terms
               convertible into or exchangeable for Common Stock (whether or not
               at the time so convertible or exchangeable) 

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               and the consideration per share for which Common Stock may at any
               time thereafter be issuable pursuant to such options, warrants or
               other rights or pursuant to the terms of such convertible or
               exchangeable securities shall be less than the Trigger Price,
               then:

                         (1) the aggregate maximum number of shares of Common
                    Stock deliverable upon exercise of such options, warrants or
                    other rights to purchase or acquire Common Stock shall be
                    considered to have been issued at the time such options,
                    warrants or rights were granted and for a consideration
                    equal to the consideration (determined in the manner
                    provided in subclauses "a" and "b" of this clause "1"), if
                    any, received by the Company upon the grant of such options,
                    warrants or rights plus the minimum purchase price provided
                    for in such options, warrants or rights for the Common Stock
                    covered thereby;

                         (2) the aggregate maximum number of shares of Common
                    Stock deliverable upon conversion of or in exchange for any
                    such convertible or exchangeable securities, or upon the
                    exercise of options, warrants or other rights to purchase or
                    acquire such convertible or exchangeable securities and the
                    subsequent conversion or exchange thereof, shall be
                    considered to have been issued at the time such securities
                    were issued or such options, warrants or rights were granted
                    and for a consideration equal to the consideration, if any,
                    received by the Company for any such securities and related
                    options, warrants or rights (excluding any cash received on
                    account of accrued interest or accrued dividends), plus the
                    minimum additional consideration, if any, to be received by
                    the Company upon the conversion or exchange of such
                    securities and the exercise of any related options, warrants
                    or rights (the consideration in each case to be determined
                    in the manner provided in subclauses "a" and "b" of this
                    clause "1");

                         (3) on any change in the number of shares of Common
                    Stock deliverable upon exercise of any such options,
                    warrants or rights or conversion of or exchange for such
                    convertible or exchangeable securities or any change in the
                    consideration to be received by the Company upon such
                    exercise, conversion or exchange, including, but not limited
                    to, a change resulting from the anti-dilution provisions
                    thereof, the Series A Conversion Price as then in effect
                    shall forthwith be readjusted to such Series A Conversion
                    Price as would have been obtained had an adjustment been
                    made upon the grant of such options, warrants or rights not
                    exercised prior to such change, or the issuance of such
                    securities not converted or exchanged prior to such change,
                    on the basis of such change;

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                         (4) on the expiration or cancellation of any such
                    options, warrants or rights, or the termination of the right
                    to convert or exchange such convertible or exchangeable
                    securities, if the Series A Conversion Price shall have been
                    adjusted upon the grant or issuance thereof, then the Series
                    A Conversion Price shall forthwith be readjusted to such
                    Series A Conversion Price as would have been obtained had an
                    adjustment been made upon the grant or issuance of such
                    options, warrants, rights or securities on the basis of the
                    issuance of only the number of shares of Common Stock
                    actually issued upon the exercise of such options, warrants
                    or rights, or upon the conversion or exchange of such
                    securities; and


                         (5) if the Series A Conversion Price shall have been
                    adjusted upon the grant or issuance of any such options,
                    warrants, rights or convertible or exchangeable securities,
                    no further adjustment of the Series A Conversion Price shall
                    be made for the actual issuance of Common Stock upon the
                    exercise, conversion or exchange thereof;

               provided, however, that no increase in the Series A Conversion
               Price shall be made pursuant to subclauses "1", "2" or "3"of this
               subclause "c".

                    d.  Notwithstanding the foregoing provisions of this
               paragraph "E" of this Section VI, the dividend or other
               distributions of Rights to holders of Common Stock shall not be
               deemed to be the issuance of Additional Shares of Common Stock
               resulting in an adjustment to the Series A Conversion Price until
               such time as such Rights become exercisable or exchangeable for
               Common Stock.

     2. Stock Dividends. If the number of shares of Common Stock outstanding at
any time after the date of issuance of Series A Preferred Stock is increased by
a stock dividend or other distribution payable in shares of Common Stock or by a
subdivision or split-up of shares of Common Stock, then immediately after the
record date fixed for the determination of holders of Common Stock entitled to
receive such stock dividend or the effective date of such subdivision or split-
up, as the case may be, the Series A Conversion Price shall be appropriately
reduced so that the holder of any shares of Series A Preferred Stock thereafter
converted shall be entitled to receive the number of shares of Common Stock
which the holder would have received immediately following such action had such
shares of Series A Preferred Stock been converted immediately prior thereto.

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     3. Combination of Stock. If the number of shares of Common Stock
outstanding at any time after the date of issuance of Series A Preferred Stock
is decreased by a combination of the outstanding shares of Common Stock, then,
immediately after the effective date of such combination, the Series A
Conversion Price for such series shall be appropriately increased so that the
holder of any shares of Series A Preferred Stock thereafter converted shall be
entitled to receive the number of shares of Common Stock which such holder would
have received immediately following such action had such shares of Series A
Preferred Stock been converted immediately prior thereto.


     4. Reclassification. In case of any Reclassification, each share of Series
A Preferred Stock shall, after such Reclassification, be convertible into the
kind and number of shares of stock or other securities, cash or property to
which the holder of such share of Series A Preferred Stock would have been
entitled to receive if the holder owned the Common Stock issuable upon
conversion of the Series A Preferred Stock immediately prior to the occurrence
of the Reclassification; and in any such case, if necessary, the provisions set
forth herein with respect to the rights and interests thereafter of the holders
of the shares of Series A Preferred Stock shall be appropriately adjusted so as
to be applicable, as nearly as possible, to any shares of stock or other
securities, cash or property thereafter deliverable on the conversion of the
shares of Series A Preferred Stock.

     5. Adjustment Upon Payment of Dividend on Common Stock. To the extent the
Company pays a dividend on Common Stock, other than Rights or a dividend payable
in Common Stock as provided for in Section VI.E.2, the Series A Conversion Price
shall immediately be reduced (i) by the per share amount of cash dividend paid
on the Common Stock or (ii) in the case of a non-cash dividend (other than
dividends of options, warrants or other rights to purchase or acquire Common
Stock for which there has been an adjustment under Section VI.E.1.c), by the
fair value of the per share amount of such dividend as reasonably determined by
the Board.

     6. Rounding of Calculations. All calculations under this paragraph "E"
shall be made to the nearest cent or to the nearest one hundredth (1/100th) of a
share, as the case may be.

     7. Timing of Issuance of Additional Common Stock Upon Certain Adjustments.
In any case in which the provisions of this paragraph "E" shall require that an
adjustment shall become effective immediately after a record date for an event,
the Company may defer until the occurrence of such event (i) issuing to the
holder of any shares of Series A Preferred Stock converted after such record
date and before the occurrence of such event the additional shares of Common
Stock issuable upon such conversion by reason of the adjustment required by such
event over and above the shares of Common Stock issuable upon such conversion
before giving effect to such adjustment, and (ii) paying to such holder any
amount of cash

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in lieu of a fractional share of Common Stock pursuant to paragraph "C" of
Section IX hereof; provided, however, that the Company upon request shall
deliver to such holder a due bill or other appropriate instrument evidencing
such holder's right to receive such additional shares and such cash, upon the
occurrence of the event requiring such adjustment.

        F. Statement Regarding Adjustments. Whenever the Series A Conversion
     Price shall be adjusted as provided in paragraph "E" of this Section VI,
     the Company shall forthwith file, at the office of any transfer agent for
     such Series A Preferred Stock and at the principal office of the Company, a
     statement showing in detail the facts requiring such adjustment and the
     Series A Conversion Price that shall be in effect after such adjustment,
     and the Company shall also cause a copy of such statement to be sent by
     certified mail, postage prepaid, to each holder of shares of Series A
     Preferred Stock at the address appearing on the Company's records. Each
     such statement shall be signed by the Company's independent public
     accountants. Where appropriate, such copy may be given in advance and may
     be included as part of a notice required to be mailed under the provisions
     of paragraph "G" of this Section VI.

        G. Notice to Holders. In the event the Company shall propose to take any
     action of the type described in clauses "1" (but only if the action of the
     type described in clause "1" would result in an adjustment in the Series A
     Conversion Price), "2", "3, "4" or "5" of paragraph "E" of this Section VI,
     the Company shall give notice to each holder of shares of Series A
     Preferred Stock affected by such action in the manner set forth in this
     paragraph "G" of this Section VI, which notice shall specify the record
     date, if any, with respect to any such action and the approximate date on
     which such action is to take place. Such notice shall also set forth such
     facts with respect thereto as shall be reasonably necessary to indicate the
     effect of such action (to the extent such effect may be known at the date
     of such notice) on the Series A Conversion Price and the number, kind or
     class of shares or other securities or property which shall be deliverable
     or purchasable upon the occurrence of such action or deliverable upon
     conversion of shares of Series A Preferred Stock. In the case of any action
     which would require the fixing of a record date, such notice shall be given
     at least ten days prior to the date so fixed, and in the case of any other
     action, such notice shall be given at least 15 days prior to the taking of
     such proposed action. Failure to give such notice, or any defect therein,
     shall not affect the legality or validity of any such action.

        H. Treasury Stock.  For the purpose of this Section VI, the sale or
     other disposition of Common Stock theretofore held in the Company's
     treasury shall be deemed to be an issuance thereof.

        I. Costs. The Company shall pay all documentary, stamp, transfer or
     other transactional taxes attributable to the issuance or delivery of
     shares of Common Stock of the Company upon conversion of any shares of
     Series A Preferred Stock; provided, however, that the Company shall not be
     required to pay any taxes which may be payable in respect of any transfer
     involved in the issuance or delivery of any certificate for such shares in
     a name 

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     other than that of the holder of the shares of Series A Preferred Stock in
     respect of which such shares are being issued.

Section VII.  Redemption.


        A. Optional Redemption. So long as any shares of Series A Preferred
     Stock shall be outstanding and to the extent that the Company shall have
     funds legally available for such payment, the Company may, but shall not be
     obligated pursuant to this Section VII.A. to, redeem for cash any such
     outstanding shares. The redemption price of each share of Series A
     Preferred Stock so redeemed shall be an amount equal to the sum of (i) the
     product of (A) the number of shares of Common Stock into which one share of
     Series A Preferred Stock is then convertible and (B) the Series A Forced
     Conversion Price and (ii) all accrued and unpaid dividends. All accrued and
     unpaid dividends payable hereunder shall be payable whether or not earned
     or declared, to and including the applicable Optional Redemption Date.

        B. Procedure With Respect to Optional Redemption. The Company shall, not
     less than 30 days nor more than 60 days prior to the applicable redemption
     date (an "Optional Redemption Date"), mail written notice (the "Optional
     Redemption Notice"), by certified mail, postage prepaid, to each holder of
     shares of record of Series A Preferred Stock to be redeemed at such
     holder's post office address last shown on the records of the Company. The
     Optional Redemption Notice shall state: (i) the total number of shares of
     Series A Preferred Stock which the Company intends to redeem; (ii) the
     number of shares of Series A Preferred Stock which the Company intends to
     redeem from that particular holder; (iii) the applicable Optional
     Redemption Date and the applicable redemption price; and (iv) the time,
     place and manner in which the holder is to surrender to the Company the
     certificate or certificates, as the case may be, representing the shares of
     Series A Preferred Stock to be redeemed. On or before the applicable
     Optional Redemption Date, each holder of Series A Preferred Stock shall
     surrender the certificate or certificates representing such shares to the
     Company, in the manner and at the place designated in the Optional
     Redemption Notice, and thereupon the applicable redemption price for such
     shares shall be payable in immediately available funds to the order of the
     person whose name appears on such certificate or certificates as the owner
     thereof, and each surrendered certificate shall be cancelled and retired.
     In the event less than all of the shares of Series A Preferred Stock
     represented by such certificate are redeemed, a new certificate shall be
     issued representing the unredeemed shares.

        C. Mandatory Redemption. If on the twentieth anniversary of the Closing
     Date and on each anniversary of the Closing Date thereafter until the
     Series A Preferred Stock is fully retired (a "Redemption Date"), all shares
     of the Series A Preferred Stock have not been previously converted or
     redeemed and if the closing price of Common Stock into which the shares of
     any outstanding series of Series A Preferred Stock are convertible is less
     than the applicable Conversion Price for such series of Series A Preferred
     Stock for a period of 30 consecutive trading days during the immediately
     preceding 12-month period (such series of Series A Preferred Stock being
     referred to as 

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<PAGE>
 
     the "Mandatorily Redeemable Preferred Stock"), then the Company shall, at
     the option of each holder of shares of Mandatorily Redeemable Preferred
     Stock not converted or redeemed, redeem in cash the lesser of (i) one-fifth
     of the shares of the Mandatorily Redeemable Preferred Stock held of record
     by such holder or (ii) the number of shares equal to the quotient resulting
     from dividing such holder's pro rata share of the Available Cash (as
     hereinafter defined) by the redemption price per share. The term "Available
     Cash" means the lesser of (A) the amount of cash legally available for the
     redemption of stock by the Company or (B) the amount of cash available, if
     any, for the redemption of stock by the Company without materially
     disrupting the business of the Company as carried on in the normal course,
     as determined in good faith by the Board of the Company. Notwithstanding
     anything herein to the contrary, if the redemption of any shares of
     Mandatorily Redeemable Preferred Stock for which redemption has been
     demanded under this Section VII.C would result in a default, an event of
     default or an event that with the passage of time or the giving of notice,
     or both, would become a default or an event of default under any contract,
     agreement, commitment or other contractual obligation to which the Company
     is a party, bound or subject to, the Company shall not be obligated to
     redeem any of the shares of Mandatorily Redeemable Preferred Stock for
     which redemption has been demanded under this Section VII.C. A holder's pro
     rata share of Available Cash with respect to shares of Mandatorily
     Redeemable Preferred Stock for which redemption has been demanded shall be
     determined ratably based upon the respective amounts which would be payable
     on such shares if all amounts payable upon redemption of all shares for
     which redemption has been demanded were paid in full. The redemption price
     per share of the Series A Preferred Stock shall be $1,000.00 plus all
     accrued and unpaid dividends as of the applicable Redemption Date, whether
     or not earned or declared. Any holder of Series A Preferred Stock may
     exercise its option to redeem shares pursuant to this Section VII.C at any
     time after an applicable Redemption Date but prior to, and such option
     shall expire at 5:00 p.m., Houston, Texas, time on, the 30th day after the
     applicable Redemption Date.

        D. Procedure With Respect to Mandatory Redemption. A holder of
     Mandatorily Redeemable Preferred Stock may exercise its option pursuant to
     paragraph "C" of this Section VII by delivering, prior to the expiration of
     such option, written notice of redemption to the Company at its principal
     executive office, together with all certificates representing shares of
     Mandatorily Redeemable Preferred Stock to be redeemed, or the affidavit and
     indemnity referenced in paragraph "F" of Section IX hereof with respect to
     such certificates, and such transmittal forms, endorsements or stock powers
     as may reasonably be requested by the Company. Upon receipt thereof, the
     Company will promptly pay, by check or wire in immediately available funds,
     the redemption price to the registered holder at the address specified in
     the written notice of redemption, or in the event no address is specified,
     at the address of the holder as it then appears on the records of the
     Company. Subject to the terms of paragraph "C" of this Section VII, in no
     event shall the redemption price be delivered later than 60 days after
     receipt by the Company of written notice of redemption pursuant to
     paragraph "C" of this Section VII.

                                       13
<PAGE>
 
  Section VIII.  Rank. The Series A Preferred Stock shall, with respect to
dividend distributions and distributions upon the Liquidation of the Company,
rank (i) senior to all classes of Common Stock of the Company, to the Company's
Series A Junior Participating Preferred Stock and to each other class of Capital
Stock of the Company or series of preferred stock of the Company hereafter
established the terms of which do not expressly provide that it ranks senior to,
or on a parity with, the Series A Preferred Stock as to dividend distributions
or distributions upon the Liquidation of the Company (collectively referred to,
together with all classes of Common Stock of the Company, as "Junior
Securities"); (ii) on a parity with any class of Capital Stock of the Company or
series of preferred stock of the Company hereafter established the terms of
which expressly provide that such class or series will rank on a parity with the
Series A Preferred Stock as to dividend distributions or distributions upon the
Liquidation of the Company (collectively referred to as "Parity Securities");
and (iii) junior to each other class of Capital Stock of the Company or series
of preferred stock of the Company hereafter established the terms of which
expressly provide that such class or series will rank senior to the Series A
Preferred Stock as to dividend distributions or distributions upon the
Liquidation of the Corporation (collectively referred to as "Senior
Securities").

  Section IX.  General.

        A. All shares of Common Stock which may be issued upon conversion of the
     shares of Series A Preferred Stock will upon issuance by the Company be
     duly and validly issued, fully paid and nonassessable, not subject to any
     preemptive rights, and free from all taxes, liens and charges with respect
     to the issuance thereof and the Company shall take no action which will
     cause a contrary result.

        B. The section headings contained in this resolution are for reference
     purposes only and shall not affect in any way the meaning of this
     resolution.

        C. No fractional shares of Common Stock or scrip shall be issued upon
     conversion of shares of the Series A Preferred Stock. If more than one
     share of Series A Preferred Stock shall be surrendered for conversion at
     any one time by the same holder, the number of full shares of Common Stock
     issuable upon conversion thereof shall be computed on the basis of the
     aggregate number of shares of Series A Preferred Stock so surrendered.
     Instead of any fractional shares of Common Stock which would otherwise be
     issuable upon conversion of any share of Series A Preferred Stock, the
     Company shall pay a cash adjustment in respect of such fractional interest
     in an amount equal to that fractional interest of the then Current Market
     Price.

        D. The Company shall reserve at all times so long as any shares of
     Series A Preferred Stock remain outstanding, free from preemptive rights,
     out of its treasury stock or its authorized but unissued shares of Common
     Stock, or both, solely for the purpose of effecting the conversion of the
     shares of Series A Preferred Stock, sufficient shares of Common Stock to
     provide for the conversion of all outstanding shares of Series A Preferred
     Stock.

                                       14
<PAGE>
 
        E. Shares of Series A Preferred Stock which have been issued and have
     been converted, redeemed, repurchased or reacquired in any manner by the
     Company shall become authorized and unissued shares of the Company's
     undesignated preferred stock, par value $.01 per share, but shall not be
     reissued as shares of Series A Preferred Stock.

        F. Upon receipt by the Company of (i) an affidavit in form and content
     reasonably acceptable to the Company stating that the stock certificate or
     certificates representing Series A Preferred Stock have been lost, stolen
     or destroyed, and (ii) an indemnity in form and content reasonably
     acceptable to the Company that indemnifies the Company against any claim
     that may be made against the Company with respect to the certificate or
     certificates alleged to have been lost, stolen or destroyed, the Company
     shall issue a new certificate or certificates in place of any certificate
     or certificates alleged to have been lost, stolen or destroyed.

        G. All dollar amounts shall be United States dollars.

        H. The Series A Preferred Stock is hereby granted registration rights in
     accordance with the terms of Section 8 of that certain Purchase Agreement
     dated November 10, 1998, by and among John Hancock Mutual Life Insurance
     Company, Hancock Mezzanine Partners, L.P. and the Company.

                  

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                                       15
<PAGE>
 
  IN WITNESS WHEREOF, the Company has caused this certificate to be signed and
attested by its duly authorized officers this 10th day of November, 1998.


                                 OCEAN ENERGY, INC.,
                                 A Delaware corporation



                                 By:
                                     ------------------------
                                     Jonathan M. Clarkson
                                     Executive Vice President



ATTEST:



---------------------------
Robert K. Reeves, Secretary

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