<PAGE>
                                                                     EXHIBIT 3.A

                  SECOND RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                             PLAINS RESOURCES INC.
                             ---------------------


     The undersigned, being the President and Secretary of Plains Resources Inc.
(the "Corporation") a corporation organized and existing under the laws of the
State of Delaware, do hereby state and certify that:  (i) the name of the
Corporation is Plains Resources Inc.; (ii) the Corporation was originally
incorporated under the name of Alifin Resources Inc. under the original
Certificate of Incorporation filed with the Secretary of State of Delaware on
September 10, 1976; (iii) on November 9, 1995, the Board of Directors of the
Corporation duly adopted this Second Restated Certificate of Incorporation
without a vote of stockholders in accordance with the provisions of Section 245
of the General Corporation Law of the State of Delaware; (iv) this Second
Restated Certificate of Incorporation only restates and integrates and does not
further amend the provisions of the Corporation's Certificate of Incorporation
as heretofore amended or supplemented, and there is no discrepancy between those
provisions and the provisions of this Second Restated Certificate of
Incorporation; and (v) the text of the Certificate of Incorporation of the
Corporation as heretofore amended or supplemented is hereby restated to read in
full, as follows:

                 "SECOND RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                             PLAINS RESOURCES INC.
                             ---------------------

FIRST:  The name of the Corporation is PLAINS RESOURCES INC.
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SECOND:  The address of its registered office in the State of Delaware is 1013
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Centre Road, Wilmington, Delaware 19805, County of Newcastle.  The name of its
registered agent at such address is The Prentice-Hall Corporation System, Inc.

THIRD:  The nature of the business or purposes to be conducted or promoted is:
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To engage in any lawful act or activity for which corporations may be organized
under the General Corporation Law of Delaware.

FOURTH:  The total number of shares of stock which the Corporation shall have
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authority to issue is 52,000,000 shares, of which 50,000,000 shall be shares of
common stock of a par value of $.10 per share and 2,000,000 shall be shares of
preferred stock of a par value of $1.00 per share.

     The Board of Directors is expressly authorized at any time, and from time
to time, to provide for the issuance of shares of preferred stock in one or more
series, with such voting powers, full or limited or without voting powers, and
with such designations, preferences and relative, participating, option or other
special rights, and qualifications, limitations or restrictions thereof, as
shall be stated and expressed in the resolution or resolutions providing for the
issue thereof adopted by the Board of Directors, and as are not stated and
expressed in this Certificate of Incorporation, or any amendment thereto,
including (but without limiting the generality of the foregoing) the following:
<PAGE>
 
     (i)  the designation of and number of shares constituting such series;

     (ii)the dividend rate of such series, the conditions and dates upon which
     such dividends shall be payable, the preference or relation which such
     dividends shall bear to the dividends payable on any other class or classes
     or on any other series of any other class or classes of capital stock, and
     whether such dividends shall be cumulative or noncumulative;

     (iii)whether the shares of such series shall be subject to redemption by
     the Corporation, and, if made subject to such redemption, the times, prices
     and other terms and conditions of such redemption;

     (iv)the terms and amounts of any sinking fund provided for the purchase or
     redemption of the shares of such series;

     (v)the extent, if any, to which the shares of such series shall be
     convertible into or exchangeable for shares of any other class or classes
     or of any other series of any class or classes of capital stock of the
     Corporation, and, if provision be made for conversion or exchange, the
     time, prices, rates, adjustments, and other terms and conditions of such
     conversion or exchange;

     (vi)the extent, if any, to which the holders of the shares of such series
     shall be entitled to vote as a class or otherwise with respect to the
     election of directors or otherwise;

     (vii) the restrictions, if any, on the issue or reissue of any additional
     preferred stock; and

     (viii)the rights of the holders of the shares of such series upon the
     dissolution of, or upon the distribution of assets of, the Corporation.

FIFTH:  The Corporation is to have perpetual existence.
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SIXTH:  In furtherance and not in limitation of the powers conferred by statute,
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the Board of Directors is expressly authorized:

     To make, alter or repeal the Bylaws of the Corporation;

     To authorize and cause to be executed mortgages and liens upon the real and
     personal property of the Corporation;

     To set apart out of any of the funds of the Corporation available for
     dividends a reserve or reserves for any proper purpose and to abolish any
     such reserve in the manner in which it was created.

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<PAGE>
 
     By resolution passed by a majority of the whole Board, to designate one or
     more committees, each committee to consist of two or more of the directors
     of the Corporation, which, to the extent provided in the resolution or in
     the Bylaws of the Corporation, shall have and may exercise the powers of
     the Board of Directors in the management of the business and affairs of the
     Corporation, and may authorize the seal of the Corporation to be affixed to
     all papers which may require it.  Such committee or committees shall have
     such name or names as may be determined from time to time by resolution
     adopted by the Board of Directors.

     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.

SEVENTH:  Whenever a compromise or arrangement is proposed between this
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Corporation and its creditors or any class of them and/or between this
Corporation and its stockholders or any class of them, any court of equitable
jurisdiction within the State of Delaware may, on the application in a summary
way of this Corporation or of any creditor or stockholder thereof or on the
application of any receiver or receivers appointed for this Corporation under
the provisions of Section 291 of Title 8 of the Delaware Code or on the
application of trustees in dissolution or of any receiver or receivers appointed
for this Corporation under the provisions of Section 279 of Title 8 of the
Delaware Code order a meeting of the creditors or class of creditors, and/or of
the stockholders or class of stock holders of this Corporation, as the case may
be, to be summoned in such manner as the said court directs.  If a majority in
number representing three-fourths in value of the creditors or class of
creditors, and/or of the stockholders or class of stockholders of this
Corporation, as the case may be, agree to any compromise or arrangement and to
any reorganization of this Corporation as a consequence of such compromise or
arrangement, the said compromise or arrangement and the said reorganization
shall, if sanctioned by the court to which the said application has been made,
be binding on all the creditors or class of creditors, and/or on all the
stockholders or class of stockholders, of this Corporation, as the case may be,
and also on this Corporation.

EIGHTH:  Meetings of stockholders may be held within or without the State of
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Delaware, as the Bylaws may provide.  The books of the Corporation may be kept
(subject to any provisions contained in the statutes) outside the State of
Delaware at such place or places as may be designated from time to time by the
Board of Directors or in the Bylaws of the Corporation.  Elections of directors
need not be by written ballot unless the Bylaws of the Corporation shall so
provide.

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<PAGE>
 
NINTH:  The Corporation reserves the right to amend, alter, change or repeal any
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provisions contained in this Certificate of Incorporation, in the manner now or
hereafter prescribed by statute, and all rights conferred upon stockholders
herein are granted subject to this reservation.

TENTH:  No director shall be personally liable to the Corporation or its
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stockholders for monetary damages for any breach of fiduciary duty by such
director as a director.  Notwithstanding the foregoing sentence, a director
shall be liable to the extent provided by applicable law (a) for breach of the
director's duty of loyalty to the Corporation or its stockholders, (b) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (c) pursuant to Section 174 of the Delaware General
Corporation Law, or (d) for any transaction from which the director derived an
improper personal benefit.  No amendment to or repeal of this Article TENTH
shall apply to or have any effect on the liability or alleged liability of any
director of the Corporation for or with respect to any acts or omissions of such
director occurring prior to such amendment.

     The Corporation shall indemnify to the full extent authorized or permitted
by law any person made, or threatened to be made, a party to any action, suit or
proceeding (whether civil, criminal or otherwise) by reason of fact that he, his
testator or intestate, is or was a director or officer of the Corporation or by
reason of the fact that such director or officer, at the request of the
Corporation, is or was serving any other corporation, partnership, joint
venture, trust, employee benefit plan or other enterprise, in any capacity.
Nothing contained herein shall affect any rights to indemnification to which
employees other than directors and officers may be entitled by law.  The rights
to indemnification set forth in this Article TENTH shall not be exclusive of any
other rights to which any person may be entitled under any statute, provision of
the Certificate of Incorporation, Bylaw, agreement, contract, vote of
stockholders or disinterested directors or otherwise.

ELEVENTH:  Notwithstanding any other provisions of this Certificate of
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Incorporation or the Bylaws of the Corporation to the contrary, no action
required to be taken or which may be taken at any annual or special meeting of
stockholders of the Corporation may be taken by written consent without a
meeting of such stockholders, except (a) any action which may be taken solely
upon the vote or consent of holders of preferred stock, or any series thereof,
or (b) any action taken upon the signing of a consent in writing, setting forth
the action so taken, by all the stockholders of the Corporation entitled to vote
thereon.

     Notwithstanding any other provisions of this Certificate of Incorporation
or the Bylaws of the Corporation to the contrary (and notwithstanding the fact
that a lesser percentage may be specified by law, this Certificate of
Incorporation or the Bylaws of the Corporation), the affirmative vote of the
holders of eighty percent (80%) or more of the outstanding shares of Voting
Stock, voting together as a single class, shall be required to amend or repeal,
or adopt any provisions inconsistent with this Article ELEVENTH.  The term
"Voting Stock" shall mean all capital stock which by its terms may be voted on
all matters submitted to the stockholders of the Corporation, generally.

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<PAGE>
 
TWELFTH:  Subject to the rights which any class or series of stock having a
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preference over the common stock as to dividends or upon liquidation may have
with respect to directors elected by such class or series, a director may be
removed from office, without cause, only by the affirmative vote of the holders
of eighty percent (80%) or more of the outstanding shares of Voting Stock
entitled to vote for the election of such director.  The term "Voting Stock"
shall mean all capital stock which by its terms may be voted on all matters
submitted to stockholders of the Corporation, generally.

     Notwithstanding any other provisions of this Certificate of Incorporation
or the Bylaws of the Corporation to the contrary (and notwithstanding the fact
that a lesser percentage may be specified by law, this Certificate of
Incorporation or the Bylaws of the Corporation), the affirmative vote of the
holders of eighty percent (80%) or more of the outstanding shares of Voting
Stock, voting together as a single class, shall be required to amend or repeal,
or adopt any provisions inconsistent with this Article TWELFTH."

     IN WITNESS WHEREOF, we the undersigned have signed this certificate this
24th day of January, 1996.


                                    /s/ Greg L. Armstrong                
                                    -----------------------------------  
                                    Greg L. Armstrong                   
                                    President                            

ATTEST:


By: /s/ Michael R. Patterson
    ----------------------------------
     Michael R. Patterson
     Secretary

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