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Exhibit 3.1 RESTATED CERTIFICATE OF INCORPORATION OF THE HOUSTON EXPLORATION COMPANY THE HOUSTON EXPLORATION COMPANY (the Corporation), a corporation organized and
existing under and by virtue of the General Corporation Law of the State of Delaware
(DGCL), hereby certifies as follows pursuant to Sections 242 and 245 of the DGCL: FIRST:
    
    The name of the Corporation is The Houston Exploration Company.SECOND:
    
    The Corporation was originally incorporated under the name of
Brooklyn Union Exploration Company, Inc.THIRD:
    
    The original Certificate of Incorporation of the Corporation was
filed in the Office of the Secretary of State of the State of
Delaware (the Secretary of State) on December 16, 1985.FOURTH:
    
    The Corporation filed amendments to its Certificate of
Incorporation with the Secretary of State on August 1, 1994 and
September 19, 1995.FIFTH:
    
    The sole stockholder of the Corporation is THEC Holdings Corp.
(the Sole Stockholder), a Delaware corporation.SIXTH:
    
    The board of directors of the Corporation, in accordance with
Sections 242 and 245 of the DGCL, (i) adopted and approved this
Restated Certificate of Incorporation (including the amendments
to the Corporations Certificate of Incorporation effected
hereby) and (ii) proposed that the Sole Stockholder adopt and
approve this Restated Certificate of Incorporation (including
the amendments to the Corporations Certificate of Incorporation
effected hereby).SEVENTH:
    
    The board of directors of the Sole Stockholder, in accordance
with Sections 242 and 245 of the DGCL, approved and adopted on
behalf of the Sole Stockholder this Restated Certificate of
Incorporation (including the amendments to the Corporations
Certificate of Incorporation effected hereby).EIGHTH:
    
    The Sole Stockholder, in accordance with Section 228 of the
DGCL, approved and adopted this Restated Certificate of
Incorporation (including the amendments to the Corporations
Certificate of Incorporation effected hereby).NINTH:
    
    This Restated Certificate of Incorporation shall become
effective upon its filing with the Secretary of State.TENTH:
    
    Effective immediately upon the filing of this Restated
Certificate of Incorporation in the office of the Secretary of
State, each outstanding share of previously existing Common
Stock shall be and hereby is converted into and reclassified as
2.47 shares of Common Stock. Certificates representing
reclassified shares are hereby canceled and upon presentation of
the canceled certificates to the Corporation, the holders
thereof shall be entitled to receive certificate(s) representing
the new shares into which such canceled shares have been
converted.ELEVENTH:
    
    The Certificate of Incorporation of the Corporation is hereby
amended and restated to read in its entirety as follows:




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ARTICLE I Name The name of the Corporation is The Houston Exploration Company. ARTICLE II Registered Office and Registered Agent The registered office of the Corporation in the State of Delaware is located at Corporation
Trust Center, 1209 Orange Street in the City of Wilmington, County of New Castle. The name of the
registered agent of the Corporation at such address is The Corporation Trust Company. ARTICLE III Purpose The purpose for which the Corporation is organized is to engage in any lawful acts and
activities for which corporations may be organized under the General Corporation Law of the State
of Delaware (DGCL), and the Corporation shall have the power to perform all lawful acts
and activities. ARTICLE IV Capitalization Section 4.01 Authorized Capital. (a) The total number of shares of stock
that the Corporation shall have the authority to issue is 55,000,000 shares of capital stock,
consisting of (i) 5,000,000 shares of preferred stock, par value $0.01 per share (the Preferred
Stock), and (ii) 50,000,000 shares of common stock, par value $0.01 per share (the Common
Stock). (b) Subject to the provisions of this Certificate of Incorporation and the Preferred
Stock Designation (as defined below) creating any series of Preferred Stock, the Corporation may
issue shares of its capital stock from time to time for such consideration (not less than the par
value thereof) as may be fixed by the Board of Directors of the Corporation (the Board of
Directors), which is expressly authorized to fix the same in its absolute discretion subject
to the foregoing conditions. Shares so issued for which the consideration shall have been paid or
delivered to the Corporation shall be deemed fully paid stock and shall not be liable to any
further call or assessment thereon, and the holders of such shares shall not be liable for any
further payments in respect of such shares. (c) The right to cumulate votes for the election of directors as provided in Section
214 of the DGCL shall not be granted and is hereby expressly denied. Section 4.02 Preferred Stock. (a) The Preferred Stock may be issued from
time to time in one or more series. Authority is hereby expressly granted to and vested in the
Board of Directors to authorize from time to time the issuance of Preferred Stock in one or more
series. With respect to each series of Preferred Stock authorized by it, the Board of Directors
shall be authorized to establish by resolution or resolutions, and by filing a certificate pursuant
to applicable law of the State of Delaware (the Preferred Stock Designation), the following to
the fullest extent now or hereafter permitted by the DGCL: (1) the designation of such series; (2) the number of shares to constitute such series; (3) whether such series is to have voting rights (full, special or limited) or is to be
without voting rights; 2




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(4) if such series is to have voting rights, whether or not such series is to be
entitled to vote as a separate class either alone or together with the holders of the Common
Stock or one or more other series of Preferred Stock; (5) the preferences and relative, participating, optional, conversion or other special
rights (if any) of such series and the qualifications, limitations or restrictions (if any)
with respect to such series; (6) the redemption rights and price(s), if any, of such series, and whether or not the
            shares of such series shall be subject to the operation of retirement or sinking funds to be
applied to the purchase or redemption of such shares for retirement and, if such retirement
or sinking funds or funds are to be established, the periodic amount thereof and the terms
and provisions relative to the operation thereof; (7) the dividend rights and preferences (if any) of such series, including, without
limitation, (i) the rates of dividends payable thereon, (ii) the conditions upon which and
the time when such dividends are payable, (iii) whether or not such dividends shall be
cumulative or noncumulative and, if cumulative, the date or dates from which such dividends
shall accumulate and (iv) whether or not the payment of such dividends shall be preferred to
the payment of dividends payable on the Common Stock or any other series of Preferred Stock; (8) the preferences (if any), and the amounts thereof, which the holders of such series
shall be entitled to receive upon the voluntary or involuntary liquidation, dissolution or
winding-up of, or upon any distribution of the assets of, the Corporation; (9) whether or not the shares of such series, at the option of the Corporation or the
holders thereof or upon the happening of any specified event, shall be convertible into or
exchangeable for (i) shares of Common Stock, (ii) shares of any other series of Preferred
Stock or (iii) any other stock or securities of the Corporation; (10) if such series is to be convertible or exchangeable, the price or prices or ratio
or ratios or rate or rates at which such conversion or exchange may be made and the terms
and conditions (if any) upon which such price or prices or ratio or ratios or rate or rates
may be adjusted; and (11) such other rights, powers and preferences with respect to such series as may to
the Board of Directors seem advisable. Any series of Preferred Stock may vary from any other series of Preferred Stock in any or all of
the foregoing respects and in any other manner. (b) The Board of Directors may, with respect to any existing series of Preferred
Stock but subject to the Preferred Stock Designation creating such series, (i) increase the number
of shares of Preferred Stock designated for such series by a resolution adding to such series
authorized and unissued shares of Preferred Stock not designated for any other series and (ii)
decrease the number of shares of Preferred Stock designated for such series by a resolution
subtracting from such series shares of Preferred Stock designated for such series (but not below
the number of shares of such series then outstanding), and the shares so subtracted shall become
authorized, unissued and undesignated shares of Preferred Stock. (c) No vote of the holders of the Common Stock or the Preferred Stock shall, unless
otherwise expressly provided in a Preferred Stock Designation creating any series of Preferred
Stock, be a prerequisite to the issuance of any shares of any series of the Preferred Stock
authorized by and complying with the conditions of this Certificate of Incorporation. Shares of
any series of Preferred Stock that have been authorized for issuance pursuant to this Certificate
of Incorporation and that have been issued and reacquired in any manner by the Corporation
(including upon conversion or exchange thereof) shall be restored to the status of authorized and
unissued shares of Preferred Stock and may be reissued as part of a new series of Preferred Stock
to be created by resolution or resolutions of the Board of Directors and a Preferred Stock
Designation as set forth above. 3




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Section 4.03 Common Stock. (a) The holders of shares of the Common Stock
shall be entitled to vote upon all matters submitted to a vote of the common stockholders of the
Corporation and shall be entitled to one vote for each share of the Common Stock held. (b) Subject to the prior rights and preferences (if any) applicable to shares of
Preferred Stock of any series, the holders of shares of the Common Stock shall be entitled to
receive such dividends (payable in cash, stock or otherwise) as may be declared thereon by the
Board of Directors at any time and from time to time out of any funds of the Corporation legally
available therefor. (c) In the event of any voluntary or involuntary liquidation, dissolution or
winding-up of the Corporation, after payment or provision for payment of the debts and other
liabilities of the Corporation and subject to the preferential or other rights (if any) of the
holders of shares of the Preferred Stock in respect thereof, the holders of shares of the Common
Stock shall be entitled to receive all the remaining assets of the Corporation available for
distribution to its stockholders, ratably in proportion to the number of shares of the Common Stock
held by them. For purposes of this paragraph (c), a liquidation, dissolution or winding-up of the
Corporation shall not be deemed to be occasioned by or to include (i) any consolidation or merger
of the Corporation with or into another corporation or other entity or (ii) a sale, lease, exchange
or conveyance of all or a part of the assets of the Corporation. Section 4.04 Stock Options, Warrants, etc. Unless otherwise expressly
prohibited in the Preferred Stock Designation creating any series of Preferred Stock, the
Corporation shall have authority to create and issue warrants, rights and options entitling the
holders thereof to purchase from the Corporation shares of the Corporations capital stock of any
class or series or other securities of the Corporation for such consideration and to such persons,
firms or corporations as the Board of Directors, in its sole discretion, may determine, setting
aside from the authorized but unissued stock of the Corporation the requisite number of shares for
issuance upon the exercise of such warrants, rights or options. Such warrants, rights and options
shall be evidenced by one or more instruments approved by the Board of Directors. The Board of
Directors shall be empowered to set the exercise price, duration, time for exercise and other terms
of such warrants, rights or options; provided however, that the consideration to be received for
any shares of capital stock subject thereto shall not be less than the par value thereof. ARTICLE V Directors Section 5.01 Number and Term. The number of directors of the Corporation
shall from time to time be fixed exclusively by the Board of Directors in accordance with, and
subject to the limitations set forth in, the bylaws of the Corporation (the Bylaws); provided,
however, that the Board of Directors shall at all times consist of a minimum of three and a maximum
of fifteen members, subject, however, to increases above fifteen members as may be required in
order to permit the holders of any series of Preferred Stock to exercise their right (if any) to
elect additional directors under specified circumstances. No decrease in the number of directors
shall have the effect of shortening the term of any incumbent director. Anything in this
Certificate of Incorporation or the Bylaws to the contrary notwithstanding, each director shall
hold office until his successor is elected and qualified or until his earlier death, resignation or
removal. Section 5.02 Classification. The Board of Directors shall be divided into
three classes designated as Class I, Class II and Class III, respectively, all as nearly equal in
number as possible, with each director then in office receiving the classification to be determined
with respect to such director by the Board of Directors. The initial term of office of Class I
directors shall expire at the annual meeting of the Corporations stockholders in 1997. The
initial term of office of Class II directors shall expire at the annual meeting of stockholders in
1998. The initial term of office of Class III directors shall expire at the annual meeting of
stockholders in 1999. Each director elected at an annual meeting of stockholders to succeed a
director whose term is then expiring shall hold office until the third annual meeting of
stockholders after his election or until his successor is elected and qualified or until his
earlier death, resignation or removal. Increases and decreases in the number of directors shall be
apportioned among the classes of directors so that all classes will be as nearly equal in number as
possible. 4




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Section 5.03 Nomination and Election. (a) Nominations of persons for
election or reelection to the Board of Directors may be made by or at the direction of the Board of
Directors. The Bylaws may set forth procedures for the nomination of persons for election or
reelection to the Board of Directors and only persons who are nominated in accordance with such
procedures (if any) shall be eligible for election or reelection as directors of the Corporation;
provided, however, that such procedures shall not infringe upon (i) the right of the Board of
Directors to nominate persons for election or reelection to the Board of Directors or (ii) the
rights of the holders of any class or series of Preferred Stock, voting separately by class or
series, to elect additional directors under specified circumstances. (a) Each director shall be elected in accordance with this Certificate of
Incorporation, the Bylaws and applicable law. Election of directors by the Corporations
stockholders need not be by written ballot unless the Bylaws so provide. Section 5.04 Removal. No director of any class may be removed before the
expiration of his term of office except for cause and then only by the affirmative vote of the
holders of not less than a majority in voting power of all the outstanding shares of capital stock
of the Corporation entitled to vote generally in an election of directors, voting together as a
single class. The Board of Directors may not remove any director, and no recommendation by the
Board of Directors that a director be removed may be made to the Corporations stockholders unless
such recommendation is set forth in a resolution adopted by the affirmative vote of not less than
two-thirds of the whole Board of Directors. Section 5.05 Vacancies. (a) In case any vacancy shall occur on the Board of
Directors because of death, resignation or removal, such vacancy may be filled only by a majority
(or such higher percentage as may be specified in the Bylaws) of the directors remaining in office
(though less than a quorum), and the director so appointed shall serve for the unexpired term of
his predecessor or until his successor is elected and qualified or until his earlier death,
resignation or removal. If there are no directors then in office, an election of directors may be
held in the manner provided by applicable law. (b) Any newly-created directorship
resulting from any increase in the number of directors may be filled only by a majority (or such
higher percentage as may be specified in the Bylaws) of the directors then in office (though less
than a quorum), and the director so appointed shall be assigned to such class of directors as such
majority of directors shall determine; provided, however, that newly-created directorships shall be
apportioned among the classes of directors so that all classes will be as nearly equal in number as
possible. Each director so appointed shall hold office for the remaining term of the class to
which he is assigned or until his successor is elected and qualified or until his earlier death,
resignation or removal. (c) Except as expressly provided in this Certificate of Incorporation or as
otherwise provided by applicable law, stockholders of the Corporation shall not have the right to
fill vacancies on the Board of Directors, including newly-created directorships. Section 5.06 Subject to Rights of Holders of Preferred Stock.
Notwithstanding the foregoing provisions of this Article V, if the Preferred Stock Designation
creating any series of Preferred Stock entitles the holders of such Preferred Stock, voting
separately by class or series, to elect additional directors under specified circumstances, then
all provisions of such Preferred Stock Designation relating to the nomination, election, term of
office, removal, filling of vacancies and other features of such directorships shall, as to such
directorships, govern and control over any conflicting provisions of this Article V, and such
directors so elected need not be divided into classes pursuant to this Article V unless expressly
provided by the provisions of such Preferred Stock Designation. Section 5.07 Limitation of Personal Liability. (a) No person who is or was
a director of the Corporation shall be personally liable to the Corporation or its stockholders for
monetary damages for breach of fiduciary duty as a director, except for liability (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) under Section 174 of the DGCL or (iv) for any transaction from which the director derived an
improper personal benefit. (b) If the DGCL is hereafter amended to authorize corporate action further limiting
or eliminating the personal liability of directors, then the personal liability of the directors to
the Corporation or its stockholders shall be limited or eliminated to the full extent permitted by
the DGCL, as so amended from time to time. 5




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ARTICLE VI Amendment of Bylaws The Board of Directors is expressly authorized and empowered to adopt, alter, amend or repeal
the Bylaws. Stockholders of the Corporation shall have the power to alter, amend, expand or repeal
the Bylaws but only by the affirmative vote of the holders of not less than 66-2/3% in voting power
of all outstanding shares of capital stock of the Corporation entitled to vote generally at an
election of directors, voting together as a single class. ARTICLE VII Actions and Meetings of Stockholders Section 7.01 No Action by Written Consent. No action shall be taken by the
stockholders of the Corporation except at an annual or special meeting of stockholders.
Stockholders of the Corporation may not act by written consent in lieu of a meeting. Section 7.02 Meetings. (a) Meetings of the stockholders of the Corporation
(whether annual or special) may only be called by the Board of Directors or by such officer or
officers of the Corporation as the Board of Directors may from time to time authorize to call
meetings of the stockholders of the Corporation. Stockholders of the Corporation shall not be
entitled to call any meeting of stockholders or to require the Board of Directors or any officer or
officers of the Corporation to call a meeting of stockholders except as otherwise expressly
provided in the Bylaws or in the Preferred Stock Designation creating any series of Preferred
Stock. (b) Stockholders of the Corporation shall not be entitled to propose business for
consideration at any meeting of stockholders except as otherwise expressly provided in the Bylaws
or in the Preferred Stock Designation creating any series of Preferred Stock. (c) Business transacted at any special meeting of stockholders shall be limited to
the purposes stated in the notice or waivers of notice of such meeting. The person presiding at a
meeting of stockholders may determine whether business has been properly brought before the meeting
and, if the facts so warrant, such person may refuse to transact any business at such meeting which
has not been properly brought before such meeting. Section 7.03 Appoint and Remove Officers, etc. The stockholders of the
Corporation shall have no right or power to appoint or remove officers of the Corporation nor to
abrogate the power of the Board of Directors to elect and remove officers of the Corporation. The
stockholders of the Corporation shall have no power to appoint or remove directors as members of
committees of the Board of Directors nor to abrogate the power of the Board of Directors to
establish one or more such committees or the power of any such committee to exercise the powers and
authority of the Board of Directors. ARTICLE VIII Indemnification of Directors and Officers The Corporation shall indemnify, to the fullest extent permitted by applicable law and
pursuant to the Bylaws, each person who is or was a director or officer of the Corporation, and may
indemnify each employee and agent of the Corporation and all other persons whom the Corporation is
authorized to indemnify under the provisions of the DGCL. ARTICLE IX Election to be Governed by Section 203 of the DGCL The Corporation hereby elects to be governed by Section 203 of the DGCL; provided however,
that the provisions of this Article IX shall not apply to restrict a business combination between
the Corporation and an interested stockholder (as defined in Section 203 of the DGCL) of the
Corporation if either (i) such business 6




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combination was approved by the Board of Directors prior to the time that such stockholder
became an interested stockholder or (ii) such stockholder became an interested stockholder as a
result of, and at or prior to the effective time of, a transaction which was approved by the Board
of Directors prior to the time that such stockholder became an interested stockholder. ARTICLE X Amendment of Certificate of Incorporation The Corporation reserves the right to amend, alter, change or repeal any provisions contained
in this Certificate of Incorporation, in the manner now or hereafter prescribed by applicable law,
and all rights conferred upon stockholders, directors or any other persons by or pursuant to this
Certificate of Incorporation are granted subject to this reservation. Notwithstanding the
foregoing or any other provision of this Certificate of Incorporation or any provision of law that
might otherwise permit a lesser or no vote, the provisions of this Article X and of Articles V, VI
and VII may not be repealed or amended in any respect, and no provision inconsistent with any such
provision or imposing cumulative voting in the election of directors may be added to this
Certificate of Incorporation, unless such action is approved by the affirmative vote of the holders
of not less than 66-2/3% in voting power of all outstanding shares of capital stock of the
Corporation entitled to vote generally at an election of directors, voting together as a single
class; provided however, that any amendment or repeal of Section 5.01 or Article VIII of this
Certificate of Incorporation shall not adversely affect any right or protection existing thereunder
in respect of any act or omission occurring prior to such amendment or repeal and, provided
further, that no Preferred Stock Designation shall be amended after the issuance of any shares of
the Series of Preferred Stock created thereby, except in accordance with the terms of such
Preferred Stock Designation and the requirements of applicable law. ARTICLE XI Voting Requirements Not Exclusive The voting requirements contained in this Certificate of Incorporation shall be in addition to
the voting requirements imposed by law or by the Preferred Stock Designation creating any series of
Preferred Stock. IN WITNESS WHEREOF, this Restated Certificate of Incorporation has been executed for and on
behalf and in the name of the Corporation by its officers thereunto duly authorized on September
18, 1996. /s/ JAMES G. FLOYDJames G. Floyd, President
 /s/ JAMES F. WESTMORELANDJames F. Westmoreland, Secretary




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CERTIFICATE OF CORRECTION THE HOUSTON EXPLORATION COMPANY THE HOUSTON EXPLORATION COMPANY (the Corporation), a corporation organized and
existing under and by virtue of the General Corporation Law of the State of Delaware
(DGCL), hereby files this Certificate of Correction pursuant to Section 103(f) of the
DGCL and certifies as follows: FIRST:
    
    The name of the Corporation is The Houston Exploration Company.SECOND:
    
    The Restated Certificate of Incorporation of the Corporation was filed in the Office of the
Secretary of State of the State of Delaware (the Secretary of State) on September 18, 1996 (the
Restated Charter).THIRD.
    
    Article TENTH of the Restated Charter contained an inaccurate conversion ratio.FOURTH.
    
    Article TENTH of the Restated Charter is hereby corrected to read in its entirety as follows:
 TENTH:
    
    Effective immediately upon the filing of this
Restated Certificate of Incorporation in the
office of the Secretary of State, each
outstanding share of previously existing
Common Stock shall be and hereby is converted
into and reclassified as that number of shares
of Common Stock such that there will be
15,295,215 shares of Common Stock outstanding
after such conversion and reclassification.
Certificates representing reclassified shares
are hereby canceled and upon presentation of
the canceled certificates to the Corporation,
the holders thereof shall be entitled to
receive certificate(s) representing the new
shares into which such canceled shares have
been converted.
 IN WITNESS WHEREOF, this Certificate of Correction has been executed for and on behalf and in
the name of the Corporation by its officer thereunto duly authorized on September 19, 1996. /s/ JAMES F. WESTMORELANDJames F. Westmoreland, Secretary




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CERTIFICATE OF AMENDMENT
TO THE
RESTATED CERTIFICATE OF INCORPORATION
OF
THE HOUSTON EXPLORATION COMPANY THE HOUSTON EXPLORATION COMPANY (the Corporation), a corporation organized and
existing under and by virtue of the General Corporation Law of the State of Delaware
(DGCL), hereby certifies: FIRST: That in lieu of a meeting and vote of directors, the Board of Directors of the
Corporation, by unanimous written consent filed with the minutes of proceedings of the Board of
Directors of the Corporation in accordance with the provisions of Section 141(f) of the DGCL,
adopted resolutions approving and declaring advisable the following amendment to the Certificate of
Incorporation of the Corporation: NOW, THEREFORE, BE IT RESOLVED, that Article V of the Restated Certificate of Incorporation of
the Corporation be amended to read in its entirety as follows: ARTICLE V Directors Section 5.01. Number. The number of directors of the Corporation shall from time to
time be fixed exclusively by the Board of Directors in accordance with, and subject to the
limitations set forth in, the bylaws of the Corporation (the Bylaws); provided, however,
that the Board of Directors shall at all times consist of a minimum of three and a maximum of
fifteen members, subject, however, to increases above fifteen members as may be required in order
to permit the holders of any series of Preferred Stock to exercise their right (if any) to elect
additional directors under specified circumstances. Section 5.02. Term. All of the directors of the Corporation shall be elected to
serve for the term set forth in the Bylaws and, anything in this Certificate of Incorporation or
the Bylaws to the contrary notwithstanding, each director shall hold office until his successor is
elected and qualified or until his earlier death, resignation or removal. Any director elected or
appointed to fill a vacancy shall hold office for the remaining term. No decrease in the number of
directors constituting the Corporations Board of Directors shall shorten the term of any incumbent
director. Section 5.03. Nomination and Election. (a) Nominations of persons for election or
reelection to the Board of Directors may be made by or at the direction of the Board of Directors.
The Bylaws may set forth procedures for the nomination of persons for election or reelection to the
Board of Directors and only persons who are nominated in accordance with such procedures (if any)
shall be eligible for election or reelection as directors of the Corporation; provided, however,
that such procedures shall not infringe upon (i) the right of the Board of Directors to nominate
persons for election or reelection to the Board of Directors or (ii) the rights of the holders of
any class or series of Preferred Stock, voting separately by class or series, to elect additional
directors under specified circumstances. (b) Each director shall be elected in accordance with this Certificate of Incorporation, the
Bylaws and applicable law. Election of directors by the Corporations stockholders need not be by
written ballot unless the Bylaws so provide. Section 5.04. Removal. No director of any class may be removed before the expiration
of his term of office except for cause and then only by the affirmative vote of the holders of not
less than a majority in voting power of all the outstanding shares of capital stock of the
Corporation entitled to vote generally in an election of directors, voting together as a single
class. The Board of Directors may not remove any director, and no recommendation by the Board of
Directors that a director be removed may be made to the Corporations stockholders unless such
recommendation is set forth in a resolution adopted by the affirmative vote of not less than
two-thirds of the whole Board of Directors.




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Section 5.05. Vacancies. (a) In case any vacancy shall occur on the Board of
Directors because of death, resignation or removal, such vacancy may be filled only by a majority
(or such higher percentage as may be specified in the Bylaws) of the directors remaining in office
(though Iess than a quorum), and the director so appointed shall serve for the unexpired term of
his predecessor or until his successor is elected and qualified or until his earlier death,
resignation or removal. If there are no directors then in office, an election of directors may be
held in the manner provided by applicable law. (b) Any newly-created directorship resulting from any increase in the number of directors may
be filled only by a majority (or such higher percentage as may be specified in the Bylaws) of the
directors then in office (though less than a quorum). Each director so appointed shall hold office
for the remainder of the term or until his successor is elected and qualified or until his earlier
death, resignation or removal. (c) Except as expressly provided in this Certificate of Incorporation or as otherwise provided
by applicable law, stockholders of the Corporation shall not have the right to fill vacancies on
the Board of Directors, including newly-created directorships. Section 5.06. Subject to Rights of Holders of Preferred Stock. Notwithstanding the
foregoing provisions of this Article V, if the Preferred Stock Designation creating any series of
Preferred Stock entitles the holders of such Preferred Stock, voting separately by class or series,
to elect additional directors under specified circumstances, then all provisions of such Preferred
Stock Designation relating to the nomination, election, term of office, removal, filling of
vacancies and other features of such directorships shall, as to such directorships, govern and
control over any conflicting provisions of this Article V. Section 5.07. Limitation of Personal Liability. (a) No person who is or was a
director of the Corporation shall be personally liable to the Corporation or its stockholders for
monetary damages for breach of fiduciary duty as a director, except for liability (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) under Section 174 of the DGCL or (iv) for any transaction from which the director derived an
improper personal benefit. (b) If the DGCL is hereafter amended to authorize corporate action further limiting or
eliminating the personal liability of directors, then the personal liability of the directors to
the Corporation or its stockholders shall be limited or eliminated to the full extent permitted by
the DGCL, as so amended from time to time. SECOND: That at the annual meeting of stockholders of the Corporation on April 24, 1997, a
two-thirds majority of the voting power of all outstanding capital stock of the Corporation
entitled to vote generally at an election of directors voted in favor of such amendment, in
accordance with the provisions of Article X of the Companys Restated Certificate of Incorporation
and Section 242 of the DGCL. THIRD: That said amendment was duly adopted in accordance with the provisions of Sections 141
and 242 of the DGCL. IN WITNESS WHEREOF, The Houston Exploration Company has caused this Certificate of Amendment
to its Restated Certificate of Incorporations to be signed by its President and attested by its
Secretary this 24th day of April, 1997. Attest:
    
    THE HOUSTON EXPLORATION COMPANY/s/ JAMES F. WESTMORELAND
    
    By: /s/ JAMES G. FLOYDJames F. Westmoreland, Secretary
    
    James G. Floyd, President




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CERTIFICATE OF DESIGNATION of SERIES A JUNIOR PARTICIPATING PREFERRED STOCK of THE HOUSTON EXPLORATION COMPANY Pursuant to Section 151 of the General Corporation Law
of the State of Delaware The Houston Exploration Company, a corporation organized and existing under the General
Corporation Law of the State of Delaware (the Corporation), in accordance with the provisions of
Section 103 thereof, DOES HEREBY CERTIFY: That pursuant to the authority vested in the Board of Directors of the Corporation (the Board
of Directors) in accordance with the provisions of the Restated Certificate of Incorporation of
the said Corporation, the said Board of Directors on August 12, 2004 adopted the following
resolution creating a series of 400,000 shares of Preferred Stock designated as Series A Junior
Participating Preferred Stock: RESOLVED, that pursuant to the authority vested in the Board of
Directors of this Corporation in accordance with the provisions of the
Restated Certificate of Incorporation, a series of Preferred Stock, par
value $0.01 per share, of the Corporation be and hereby is created, and
that the designation and number of shares thereof and the voting and other
powers, preferences and relative, participating, optional or other rights
of the shares of such series and the qualifications, limitations and
restrictions thereof are as follows: Series A Junior Participating Preferred Stock 1. Designation and Amount.There shall be a series of Preferred Stock that shall be
designated as Series A Junior Participating Preferred Stock, and the number of shares
constituting such series shall be 400,000. Such number of shares may be increased or decreased by
resolution of the Board of Directors; provided, however, that no decrease shall reduce the number
of shares of Series A Junior Participating Preferred Stock to less than the number of shares then
issued and outstanding plus the number of shares issuable upon exercise of outstanding rights,
options or warrants or upon conversion of outstanding securities issued by the Corporation. 2. Dividends and Distribution. (A) Subject to the prior and superior rights of the holders of any shares of any class or
series of stock of the Corporation ranking prior and superior to the shares of Series A Junior
Participating Preferred Stock with respect to dividends, the holders of shares of Series A Junior
Participating Preferred Stock, in preference to the holders of shares of any class or series of
stock of the Corporation ranking junior to the Series A Junior Participating Preferred Stock in
respect thereof, shall be entitled to receive, when, as and if declared by the Board of Directors
out of funds legally available for the purpose, quarterly dividends payable in cash on the final
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 Junior Participating
Preferred Stock, in an amount per share (rounded to the nearest cent) equal to the greater of (a)
$10.00 or (b) the Adjustment Number (as defined below) times the aggregate per share amount of all
cash dividends, and the Adjustment Number times the aggregate per share amount (payable in kind) of
all non-cash dividends or other distributions other than a dividend payable in shares of Common
Stock or




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a subdivision of the outstanding shares of Common Stock (by reclassification or otherwise),
declared on the Common Stock, par value $0.01 per share, of the Corporation (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 Junior Participating Preferred Stock. The Adjustment Number shall initially be 1000.
In the event the Corporation shall at any time after August 23, 2004 (i) declare and pay any
dividend on Common Stock payable in shares of Common Stock, (ii) subdivide the outstanding Common
Stock or (iii) combine the outstanding Common Stock into a smaller number of shares, then in each
such case the Adjustment Number in effect immediately prior to such event shall be adjusted by
multiplying such Adjustment Number 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 Corporation shall declare a dividend or distribution on the Series A Junior
Participating Preferred Stock as provided in paragraph (A) above immediately after it declares a
dividend or distribution on the Common Stock (other than a dividend payable in shares of Common
Stock). (C) Dividends shall begin to accrue and be cumulative on outstanding shares of Series A Junior
Participating Preferred Stock from the Quarterly Dividend Payment Date next preceding the date of
issue of such shares of Series A Junior Participating Preferred Stock, unless the date of issue 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 issue of such shares, or
unless the date of issue is a Quarterly Dividend Payment Date or is a date after the record date
for the determination of holders of shares of Series A Junior Participating 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 Junior Participating 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 of Directors may fix
a record date for the determination of holders of shares of Series A Junior Participating Preferred
Stock entitled to receive payment of a dividend or distribution declared thereon, which record date
shall be no more than 60 days prior to the date fixed for the payment thereof. 3. Voting Rights.The holders of shares of Series A Junior Participating Preferred Stock
shall have the following voting rights: (A) Each share of Series A Junior Participating Preferred Stock shall entitle the holder
thereof to a number of votes equal to the Adjustment Number on all matters submitted to a vote of
the stockholders of the Corporation. (B) Except as required by law, by Section 3(C) and by Section 10 hereof, holders of Series A
Junior Participating 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. (C) If, at the time of any annual meeting of stockholders for the election of directors, the
equivalent of six quarterly dividends (whether or not consecutive) payable on any share or shares
of Series A Junior Participating Preferred Stock are in default, the number of directors
constituting the Board of Directors of the Corporation shall be increased by two. In addition to
voting together with the holders of Common Stock for the election of other directors of the
Corporation, the holders of record of the Series A Junior Participating Preferred Stock, voting
separately as a class to the exclusion of the holders of Common Stock, shall be entitled at said
meeting of stockholders (and at each subsequent annual meeting of stockholders), unless all
dividends in arrears on the Series A Junior Participating Preferred Stock have been paid or
declared and set apart for payment prior thereto, to vote for the election of two directors of the
Corporation, the holders of any Series A Junior Participating Preferred Stock being entitled to
cast a number of votes per share of Series A Junior Participating Preferred Stock as is specified
in paragraph (A) of this Section 3. Until the default in payments of all dividends which permitted
the election of said directors shall cease to exist, any director who shall have been so elected
pursuant to the provisions of this Section 3(C) may be removed at any time, without cause, only by
the affirmative vote of the holders of the




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shares of Series A Junior Participating Preferred Stock at the time entitled to cast a
majority of the votes entitled to be cast for the election of any such director at a special
meeting of such holders called for that purpose, and any vacancy thereby created may be filled by
the vote of such holders. If and when such default shall cease to exist, the holders of the Series
A Junior Participating Preferred Stock shall be divested of the foregoing special voting rights,
subject to revesting in the event of each and every subsequent like default in payments of
dividends. Upon the termination of the foregoing special voting rights, the terms of office of all
persons who may have been elected directors pursuant to said special voting rights shall forthwith
terminate, and the number of directors constituting the Board of Directors shall be reduced by two.
The voting rights granted by this Section 3(C) shall be in addition to any other voting rights
granted to the holders of the Series A Junior Participating Preferred Stock in this Section 3. 4. Certain Restrictions. (A) Whenever quarterly dividends or other dividends or distributions payable on the Series A
Junior Participating 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
Junior Participating Preferred Stock outstanding shall have been paid in full, the Corporation
shall not: (i) declare or pay dividends on, make any other distributions on, or redeem or purchase or
otherwise acquire for consideration any shares of stock ranking junior (either as to dividends or
upon liquidation, dissolution or winding up) to the Series A Junior Participating Preferred Stock; (ii) declare or pay dividends on 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 Junior Participating Preferred Stock, except dividends paid ratably on the Series A
Junior Participating 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; or (iii) purchase or otherwise acquire for consideration any shares of Series A Junior
Participating Preferred Stock, or any shares of stock ranking on a parity with the Series A Junior
Participating Preferred Stock, except in accordance with a purchase offer made in writing or by
publication (as determined by the Board of Directors) to all holders of Series A Junior
Participating Preferred Stock, or to such holders and holders of any such shares ranking on a
parity therewith, upon such terms as the Board of Directors, after consideration of the respective
annual dividend rates and other relative rights and preferences of the respective series and
classes, shall determine in good faith will result in fair and equitable treatment among the
respective series or classes. (B) The Corporation shall not permit any subsidiary of the Corporation to purchase or
otherwise acquire for consideration any shares of stock of the Corporation unless the Corporation
could, under paragraph (A) of this Section 4, purchase or otherwise acquire such shares at such
time and in such manner. 5. Reacquired Shares.Any shares of Series A Junior Participating Preferred Stock purchased
or otherwise acquired by the Corporation in any manner whatsoever shall be retired promptly after
the acquisition thereof. All such shares shall upon their retirement become authorized but
unissued shares of Preferred Stock and may be reissued as part of a new series of Preferred Stock
to be created by resolution or resolutions of the Board of Directors, subject to any conditions and
restrictions on issuance set forth herein. 6. Liquidation, Dissolution or Winding Up.(A) Upon any liquidation, dissolution or winding up
of the Corporation, voluntary or otherwise, no distribution shall be made to the holders of shares
of stock ranking junior (either as to dividends or upon liquidation, dissolution or winding up) to
the Series A Junior Participating Preferred Stock unless, prior thereto, the holders of shares of
Series A Junior Participating Preferred Stock shall have received an amount per share (the Series
A Liquidation Preference) equal to the greater of (i) $10.00 plus an amount equal to accrued and
unpaid dividends and distributions thereon, whether or not declared, to the date of such payment,
or (ii) the Adjustment Number times the per share amount of all cash and other property to be
distributed in respect of the Common Stock upon such liquidation, dissolution or winding up of the
Corporation. (B) In the event, however, that there are not sufficient assets available to permit payment in
full of the Series A Liquidation Preference and the liquidation preferences of all other classes
and series




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of stock of the Corporation, if any, that rank on a parity with the Series A Junior
Participating Preferred Stock in respect thereof, then the assets available for such distribution
shall be distributed ratably to the holders of the Series A Junior Participating Preferred Stock
and the holders of such parity shares in proportion to their respective liquidation preferences. (C) Neither the merger or consolidation of the Corporation into or with another entity nor the
merger or consolidation of any other entity into or with the Corporation shall be deemed to be a
liquidation, dissolution or winding up of the Corporation within the meaning of this Section 6. 7. Consolidation, Merger, Etc.In case the Corporation shall enter into any consolidation,
merger, combination or other transaction in which the outstanding 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 Junior Participating Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share equal to the Adjustment Number 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 Common Stock is changed or exchanged. 8. No Redemption.Shares of Series A Junior Participating Preferred Stock shall not be
subject to redemption by the Corporation. 9. Ranking.The Series A Junior Participating Preferred Stock shall rank junior to all other
series of the Preferred Stock as to the payment of dividends and as to the distribution of assets
upon liquidation, dissolution or winding up, unless the terms of any such series shall provide
otherwise, and shall rank senior to the Common Stock as to such matters. 10. Amendment.At any time that any shares of Series A Junior Participating Preferred Stock
are outstanding, the Certificate of Incorporation of the Corporation shall not be amended, by
merger, consolidation or otherwise, which would materially alter or change the powers, preferences
or special rights of the Series A Junior Participating Preferred Stock so as to affect them
adversely without the affirmative vote of the holders of two-thirds of the outstanding shares of
Series A Junior Participating Preferred Stock, voting separately as a class. 11. Fractional Shares.Series A Junior Participating Preferred Stock may be issued in
fractions of a share that shall entitle the holder, in proportion to such holders fractional
shares, to exercise voting rights, receive dividends, and participate in distributions and to have
the benefit of all other rights of holders of Series A Junior Participating Preferred Stock. IN WITNESS WHEREOF, the undersigned has executed this Certificate this 23rd day of August,
2004. THE HOUSTON EXPLORATION COMPANYBy:
    /s/ JAMES F. WESTMORELANDName:
    James F. WestmorelandTitle:
    Vice President and Chief Accounting Officer




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STATE OF DELAWARE
CERTIFICATE OF AMENDMENT
OF RESTATED CERTIFICATE OF INCORPORATION The Houston Exploration Company, a corporation organized and existing under and by virtue of the
General Corporate Law of the State of Delaware does hereby certify: FIRST: That at a meeting of the Board of Directors of The Houston Exploration Company, resolutions
were duly adopted setting forth a proposed amendment of the Restated Certificate of Incorporation
of said corporation, declaring said amendment to be advisable and calling a meeting of the
stockholders of said corporation for consideration thereof. The resolution setting forth the
proposed amendment is as follows: RESOLVED, that the Restated Certificate of Incorporation of this corporation be amended by
changing the Article thereof numbered Section 4.01. Authorized Capital. (a) so
that, as amended, said Article shall be and read as follows: (a) The total number of shares of stock that the Corporation shall have the authority to
issue is 105,000,000 shares of capital stock, consisting of (i) 5,000,000 shares of
preferred stock, par value $0.01 per share (the Preferred Stock), and (ii)
100,000,000 shares of common stock, par value $0.01 per share (the Common Stock). SECOND: That thereafter, pursuant to resolution of its Board of Directors, an annual meeting of
the stockholders of said corporation was duly called and held upon notice in accordance with
Section 222 of the General Corporation Law of the State of Delaware at which meeting the necessary
number of shares as required by statute were voted in favor of the amendment. THIRD: That said amendment was duly adopted in accordance with the provisions of Section 242 of
the General Corporation Law of the State of Delaware. FOURTH: That the capital of said corporation shall not be reduced under or by reason of said
amendment. IN WITNESS WHEREOF, said corporation has caused this certificate to be signed this 26th day of
April, 2005. THE HOUSTON EXPLORATION COMPANYBy:
    /s/ WILLIAM G. HARGETTWilliam G. HargettChairman, President and
Chief Executive Officer