RESTATED CERTIFICATE OF INCORPORATION
 
                                       OF
 
                             PRIMEENERGY CORPORATION
 
                            * * * * * * * * * * * * *
 
      PrimeEnergy  Corporation, a corporation organized and existing under the
laws of the State of Delaware, hereby certifies as follows:
 
      1. The name of the corporation is PrimeEnergy Corporation. The name under
which the corporation was originally incorporated was K. R. M. Petroleum
Corporation. The date of filing of its original Certificate of Incorporation
with the Secretary of State was March 22, 1973.
 
      2. This Restated Certificate of Incorporation restates and integrates and
does not further amend the provisions of the Certificate of the corporation as
heretofore amended or supplemented and there is no discrepancy between those
provisions and the provisions of this Restated Certificate of Incorporation.
 
      3. The text of the Certificate of Incorporation as amended or supplemented
heretofore is hereby restated without further amendments or changes to read as
herein set forth in full.
 
      FIRST: The name of the corporation is PrimeEnergy Corporation.
 
      SECOND: Its registered office in the State of Delaware is located at the
Corporation Trust Center, 1209 Orange Street, Wilmington, Delaware 19801. The
name and address of its registered agent is The Corporation Trust Company,
Corporation Trust Center, 1209 Orange Street, Wilmington, Delaware 19801.
 
      THIRD: The purpose of the corporation is to acquire, own, hold, deal in,
explore, develop and operate oil, gas and other mineral properties and interests
therein of all kinds; to produce, process, transport and sell the resulting
products and to purchase, lease, own, hold, deal in and operate all equipment,
machinery, facilities, systems and plants necessary for such purposes; and to
engage generally in all phases of the oil and gas business and any lawful act or
activity for which corporations may be organized under the General Law of
Delaware.
 
                                        1
<PAGE>
 
      FOURTH: The total number of shares of all classes of stock which the
corporation shall have authority to issue is Fifteen Million (15,000,000),
consisting of Ten Million (10,000,000) shares of Common Stock, par value $.10
per share, and Five Million (5,000,000) shares of Preferred Stock, par value
$.10 per share, which shares of Preferred Stock shall be issuable in one or more
series.
 
      The relative rights, preferences and limitations of each class of capital
stock, and the designation and relative rights, preferences and limitations of
each series of Preferred Stock are to be fixed as follows:
 
1.    PROVISIONS RELATING TO THE PREFERRED STOCK
 
      A. The Preferred Stock may be issued from time to time in one or more
series, each of such series to have such designation, preferences and relative,
participating, optional or other special rights and qualifications, limitations
or restrictions thereof as are stated and expressed herein and in the resolution
or resolutions providing for the issue of such series adopted by the Board of
Directors as hereinafter provided.
 
      B. Authority is hereby expressly granted to the Board of Directors,
subject to the provisions of this Article FOURTH, to authorize the issue of one
or more series of Preferred Stock and with respect to each series to fix by
resolution or resolutions providing for the issue or such series:
 
      (1) The number of shares to constitute such series and the distinctive
designation thereof;
 
      (2) The dividend rate, if any, on the shares of such series, whether or
not such dividends shall be cumulative, and, if so, the date or dates from which
dividends shall accumulate and the dates on which dividends, if declared shall
be payable;
 
      (3) Whether or not the shares of such series shall be redeemable, the
limitations and restrictions with respect to such redemptions, the manner of
selecting shares of such series for redemption if less than all shares are to be
redeemed, and the premium, if any, over and above the par value thereof and any
accrued dividends thereon which the holders of shares of such series shall be
entitled to received upon the redemption thereof, which premium may vary at
different redemption dates and may be different with respect to shares redeemed
through the operation of any retirement or sinking fund and with respect to
shares otherwise redeemed;
 
      (4) The premium, if any, over and above the par value thereof and any
accrued dividends, if any, thereon which the holders of shares of such series
shall be entitled to received upon the voluntary liquidation, dissolution or
winding up on the corporation, which premium may vary at different dates;
 
      (5) Whether or not the shares of such series shall be subject to the
operation of a purchase, retirement or sinking fund and, if so, whether such
retirement of sinking fund shall be cumulative or noncumulative, the extent to
and the manner in which such fund shall be applied to the purchase or redemption
of the shares of such series for retirement or to other corporate purposes, and
the terms
 
                                        2
<PAGE>
 
and provisions relative to the operation thereof;
 
      (6) Whether or not the shares of such series shall be convertible into, or
exchangeable for, shares of stock of any other class or classes, or of any other
series of the same class and, if so convertible or exchangeable, the price or
prices of the rate or rates of conversion or exchange and the method, if any, of
adjusting the same;
 
      (7) The voting powers, if any, of such series in addition to the voting
powers provided in paragraph F of this Section 1; and
 
      (8) Any other preferences and relative, participating, optional or other
special rights and qualifications, limitations, or restrictions thereof as shall
not be inconsistent with this Section 1.
 
      C. All shares of any one series of Preferred Stock shall be identical with
each other in all respects, except that shares of any one series issued at
different times may differ as to the date from which dividends thereon may be
cumulative; and all series shall rank equally and be identical in all respects,
except as permitted by the foregoing provisions of paragraph B of this Section
1.
 
      D. Before any dividends on any class or classes of stock of the
corporation other than the Preferred Stock (other than dividends payable in
shares of any such other class or classes of stock of the corporation) shall be
declared or paid or set apart for payment, the holders of shares of the
Preferred Stock of each series shall be entitled to cash dividends, but only
when and as declared by the Board of Directors out of funds legally available
therefor, at the rate, and no more, fixed by the resolution or resolutions
adopted by the Board of Directors providing for the issue of such series,
payable on such dates as may be fixed in such resolution or resolutions in each
year and, if cumulative, from the date or dates fixed in the resolution or
resolutions adopted by the Board of Directors providing for the issue of such
series. Dividends in full shall not be declared or paid or set apart for payment
on the Preferred Stock of any one series for any dividend period unless
dividends in full have been declared or paid or set apart for payment of the
Preferred Stock of all series for all dividend periods terminating on the same
or any earlier date. When the stated dividends are not paid in full on all
series of the Preferred Stock, the shares of all series shall share ratably in
the payment of dividends, including accumulations, if any, in accordance with
the sums which would be payable on said shares if all dividends were declared
and paid in full. A "dividend period" is the period between any two consecutive
dividend payment dates (or, when shares are originally issued, the period from
the date from which dividends are cumulative to the first dividend payment date)
as fixed for a particular series. Accruals of dividends shall not bear interest.
 
      E. In the event of any liquidation, dissolution or winding up of the
corporation, before any payment or distribution of the assets of the corporation
shall be made to or set apart for the holders of the shares of the class or
classes of stock of the corporation other than the Preferred Stock, the holders
of the shares of the Preferred Stock shall be entitled to receive payment of ten
cents ($.10) per share, plus an amount equal to all dividends accrued thereon,
if any, to the date of final distribution to such holders, and, in addition
thereto, if such liquidation, dissolution or winding up be
 
                                        3
<PAGE>
 
voluntary, the amount of the premium, if any, payable upon such liquidation,
dissolution or winding up as fixed for the shares of the respective series; but
they shall be entitled dissolution or winding up of the corporation, the assets
of the corporation, or proceeds thereof, distributable among the holders of the
shares of the Preferred Stock shall be insufficient to pay in full the
preferential amount aforesaid, then such assets, or the proceeds thereof, shall
be distributed among such holders ratably in accordance with the respective
amounts which would be payable on such shares if all amounts payable thereon
were paid in full. For the purposes of this paragraph E, 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
corporation or a consolidation or merger of the corporation with one or more
corporations shall not be deemed to be a dissolution, liquidation or winding up
voluntary or involuntary.
 
      F. So long as any of the Preferred Stock is outstanding, the corporation:
 
      (1) will not declare or pay, or set apart for payment, any dividends
(other than dividends payable in shares of any class or classes of stock of the
corporation other than the Preferred Stock), or make any distribution on any
class or classes of stock of the corporation other than the Preferred Stock, and
will not redeem, purchase or otherwise acquire, directly or indirectly, whether
voluntarily, for a sinking fund, or otherwise, any shares of any class or
classes of stock of the corporation other than the Preferred Stock, if at the
time of making such declaration, payment, setting apart, distribution,
redemption, purchase or acquisition the corporation shall be in default with
respect to any dividend payable on or any obligation to retire shares of the
Preferred Stock; provided that, notwithstanding the foregoing, the corporation
may at any time redeem, purchase, or otherwise acquire shares of stock of any
such other class or otherwise acquire shares of stock of any such other class in
exchange for, or out of the net cash proceeds from the concurrent sale of, other
shares of stock of any such other class;
 
      (2) will not, without the affirmative vote or consent of the holders of at
least a majority of all of the Preferred Stock at the time outstanding, given in
person or by proxy, either in writing or by resolution adopted at a special
meeting called for the purpose, at which the holders of the Preferred Stock,
regardless of series, shall vote separately as a class, amend, alter or repeal
(by any means, including, without limitation, merger or consolidation) any of
the provisions of this Section 1 so as adversely to affect the preferences,
rights or powers of the Preferred Stock; and
 
      (3) will not, without the affirmative vote or consent of the holders of at
least a majority of any adversely affected series of the Preferred Stock at the
time outstanding, given in person or by proxy, either in writing or by
resolution adopted at a special meeting called for the purpose (the holders of
such series of the Preferred Stock consenting or voting, as the case may be,
separately as a class), amend, alter or repeal (by any means, including, without
limitation, merger or consolidation) any of the provisions herein or in the
resolution or resolutions adopted by the Board of Directors providing for the
issue of such series so as adversely to affect the preferences, rights or powers
of the Preferred Stock of such series.
 
                                        4
<PAGE>
 
      G. If in any case the amounts payable with respect to any obligations to
retire shares of the Preferred Stock are not paid in full in the case of all
series with respect to which obligations exist, the number of shares of each of
such series to be retired pursuant to any such obligations shall be in
proportion to the respective amounts which would be payable on account of such
obligations if all amounts payable in respect to such series were discharged in
full.
 
2.    PROVISIONS RELATING TO THE COMMON STOCK
 
      A. Subject to paragraph F of Section 1 and, except as provided in this
Article FOURTH or by resolution or resolutions Board of Directors providing for
the issue of such series of Preferred Stock, the exclusive voting power for all
purposes shall be vested in the holders of Common Stock.
 
      B. Each share of the Common Stock shall entitle the holder thereof to one
vote, in person or by proxy, at any and all meetings of the stockholders of the
corporation, on all propositions before such meetings.
 
      C. All shares of the Common Stock shall have equal rights of participation
in dividends and in assets of the corporation on any liquidation after payment
to the holders of the Preferred Stock as set forth in paragraph E of Section 1.
 
      D. The judgment of the Directors as to the consideration of the issuance
of any such warrant, right, privilege or option and the sufficiency thereof
shall be conclusive. The price to be received by the corporation upon issuance
of shares upon the exercise of any such warrant, right, privilege or option
shall not be less than the par value thereof.
 
      E. Without action by the stockholders, the authorized shares of stock of
any class may be issued by the corporation from time to time for such
consideration as may be fixed by the Board of Directors, and any and all shares
issued, for which all of the consideration fixed by the Board of Directors shall
have been paid or delivered to the corporation, shall be deemed fully paid and
not liable to any further or assessment thereon, and the holder of such shares
shall not be liable for any further call or assessment thereon whatsoever.
 
      F. The corporation may from time to time create one of more series of
bonds, debentures, notes or other debt securities, bearing such voting rights as
may be determined by action or the Board of Directors upon the creation of such
series; and if such voting rights confer the right to elect one or more
Directors of the corporation, the Board of Directors shall, at the time of
authorizing such series of debt securities, amend the Bylaws of the corporation
to increase the number of Directors by the number so to be elected.
 
      G. No holder of stock of any class of the corporation shall have the
preemptive right to purchase or to subscribe for any additional issues of stock
of any class or of any other securities of the corporation or any warrants,
options or rights to purchase any such stock, or any other securities of the
corporation convertible into or exchangeable for such stock of the corporation.
 
                                        5
<PAGE>
 
      H. Stockholders of the corporation shall not be entitled to cumulative
voting.
 
      FIFTH: In furtherance and not in limitation of the powers conferred by
statute, the Board of Directors is expressly authorized:
 
      A. To make, alter or repeal the Bylaws of the corporation.
 
      B. To authorize and cause to be executed mortgages and liens upon the real
and personal property of the corporation.
 
      C. When and as authorized by the affirmative vote of the holders of a
majority of the stock issued and outstanding having voting power given at a
stockholders' meeting duly called for that purpose, or when authorized by the
written consent of the holders of a majority of the voting stock issued and
outstanding, to sell, lease, or exchange all of the property and assets of the
corporation, including its good will and its corporate franchises, upon such
terms and conditions and for such consideration, which may be in whole or in
part shares of stock in, and/or other securities of, any other corporation or
corporations, as its Board of Directors shall deem expedient and for the best
interests of the corporation.
 
      SIXTH. No Director of the corporation shall be liable to any person on
account of any action undertaken by him as such Director in reliance in good
faith upon the existence of any fact or circumstance reported or certified to
the Board of Directors by any officer of the corporation or by any independent
auditor, engineer or consultant retained or employed as such by the Board of
Directors.
 
      Any person made a party to any civil or criminal action, suit or
proceeding by reason of the fact that he, his testator or intestate, is or was a
Director, officer of employee of the corporation or any corporation which he
served as such at the request of the corporation, shall be indemnified by the
corporation against the reasonable expenses, including attorneys' fees, and
amounts paid in satisfaction of judgment or in settlement, other than amounts
paid to the corporation by him, actually and necessarily incurred by him or
imposed in connection with or resulting from the Denise of such civil or
criminal action, suit or proceeding, or in connection with any appeal therein,
except in a relation to matters as to which it shall be adjudged in such civil
or criminal action, suit or proceeding that such officer, Director or employee
is liable for negligence or misconduct in the performance of his duties. Neither
a conviction in a criminal action, suit or proceeding, whether based upon a plea
of guilty or nolo contendere or its equivalent, or after trial, nor a settlement
in any civil action, suit or proceeding shall or itself be deemed an
adjudication that such officer, Director or employee is liable for negligence or
misconduct in the performance of his duties to the corporation. Any amount
payable pursuant to this Article SIXTH may be determined and paid, at the option
of the person to be indemnified, pursuant to procedure set forth from time to
time in the Bylaws or by any of the following procedures: (a) order of the court
having jurisdiction of any such civil or criminal action, suit or proceeding,
(b) resolution adopted by a majority of a quorum of the Board of Directors of
the
 
                                        6
<PAGE>
 
corporation without counting in such majority or quorum any interested
Directors, (c) resolution adopted by the holders of record of a majority of the
outstanding shares of capital stock of the corporation having voting power, or
(d) order of any court having jurisdiction over the corporation. Such right of
indemnification shall not be exclusive of any other right which such officers,
Directors and employees of the corporation, and the corporation, and the other
persons above mentioned, may have such statement, they shall be entitled to
their respective rights of indemnification under any Bylaw, agreement, vote of
stockholders, provisions of law or otherwise as their rights under this Article
SIXTH.
 
      SEVENTH: Meetings of stockholders may be held without the State of
Delaware if the Bylaws so provide. The books of the corporation may be kept
(subject to any provision contained in the statutes) outside of the State of
Delaware at such place or places as may be from time to time designated by the
Board of Directors or the Bylaws of the corporation.
 
      EIGHTH: The corporation reserves the right to amend, alter, change or
repeal any provision contained in this Certificate of Incorporation, with the
exception of the preferences, rights and powers of the Preferred Stock which may
only be amended, altered or repealed as provided in paragraph (6) of Section A
of Article FOURTH hereof, in the manner now or hereafter prescribed by statute,
and all rights conferred herein are granted subject to this reservation.
 
      NINTH: No person serving as a Director of the corporation shall have any
personal liability to the corporation or its stockholders for monetary damages
for breach of fiduciary duty as a Director, provided that, such restriction on
personal liability shall not eliminate or limit the liability of a Director (i)
for any breach of the Director's duty of loyalty to the corporation or its
stockholders, (ii) for acts or omissions not in good faith or which involve
intentional misconduct or a knowing violation of law, (iii) for unlawful payment
of any dividend or unlawful stock purchase or redemption under Section 174 of
the Delaware General Corporation Law; or (iv) for any transaction from which the
Director derived an improper personal benefit.
 
      This Restated Certificate of Incorporation was duly adopted by the Board
of Directors of the corporation in accordance with Section 245 of the General
Corporation Law of the State of Delaware.
 
      IN WITNESS WHEREOF, PrimeEnergy Corporation has caused this Restated
Certificate of Incorporation to be signed by Charles E. Drimal, Jr., its
president, this _____ day of March, 2000.
 
                                                      PrimeEnergy Corporation
 
                                                      By________________________
                                                          Charles E. Drimal, Jr.
                                                          President
 
                                       7