<PAGE>

                                                                     EXHIBIT 4.3

                                FIRST AMENDMENT
                                       TO
                           THE PLAINS RESOURCES INC.
                                     BYLAWS


     This First Amendment to the Plains Resources Inc. Bylaws, dated as of
December 18, 1992 (the "Bylaws"), hereby amends the Bylaws as follows effective
as of May 15, 2001:

     1.  Article IV is hereby amended and restated to read in its entirety as
follows:

                                  "ARTICLE IV

                                    OFFICERS
                                    --------


     Section 1.  General.  The officers of the Corporation shall be chosen by
the Board of Directors and shall be a Chief Executive Officer, a President, a
Secretary and a Treasurer.  The Board of Directors may also choose a Chairman of
the Board of Directors (who must be a director), one or more Vice-Chairmen (who
must be directors) and one or more Vice-Presidents, Assistant Secretaries,
Assistant Treasurers and other officers.  Any number of offices may be held by
the same person, unless otherwise prohibited by law, the Certificate of
Incorporation or these Bylaws.  The officers of the Corporation need not be
stockholders of the Corporation nor, except in the case of the Chairman and any
Vice-Chairman of the Board of Directors, need such officers be directors of the
Corporation.

     Section 2.  Election.  The Board of Directors at its first meeting held
after each Annual Meeting of Stockholders shall elect the officers of the
Corporation who shall hold their offices for such terms and shall exercise such
powers and perform such duties as shall be determined from time to time by the
Board of Directors; and all officers of the Corporation shall hold office until
their successors are chosen and qualified, or until their earlier resignation or
removal by the Chief Executive Officer or the Board of Directors.  Any officer
elected by the Board of Directors may be removed at any time by action of the
Chief Executive Officer or by the affirmative vote of a majority of the Board of
Directors.  Any vacancy occurring in any office of the Corporation shall be
filled by the Board of Directors.  The salaries of all officers of the
Corporation shall be fixed by the Board of Directors or a duly authorized
committee thereof.

     Section 3.  Voting Securities Owned by the Corporation.  Powers of
attorney, proxies, waivers of notice of meeting, consents and other instruments
relating to securities owned by the Corporation may be executed in the name of
and on behalf of the Corporation by the Chief Executive Officer, the President
or any Vice-President, and any such officer may, in the name of and on behalf of
the Corporation, take all such action as any such officer may deem advisable to
vote in person or by proxy at any meeting of security holders of any corporation
in which the
<PAGE>

Corporation may own securities and at any such meeting shall possess and may
exercise any and all rights and power incident to the ownership of such
securities and which, as the owner thereof, the Corporation might have exercised
and possessed if present. The Board of Directors may, by resolution, from time
to time confer like powers upon any other person or persons.

     Section 4.  Duties.  The officers of the Corporation shall have such powers
and duties as generally pertain to their officers, except as modified herein or
by the Board of Directors or the Chief Executive Officer.  The Chairman of the
Board, if there is one, shall have such duties as may be assigned to him by the
Board of Directors and shall preside at meetings of the Board of Directors and
at meetings of the stockholders.  The Chief Executive Officer shall be the chief
executive officer of the Corporation and shall have the general supervision over
the business, affairs and property of the Corporation. The Secretary and
Assistant Secretary of the Corporation shall record all proceedings at meetings
and actions in writing of stockholders, directors and committee of directors,
and shall exercise such additional authority and perform such additional duties
as the Board of Directors or the Chief Executive Officer may assign."

     2.  As amended and restated by the foregoing, the Bylaws shall remain in
full force and effect.


                               PLAINS RESOURCES INC.


                               By: /s/ James C. Flores
                                   -----------------------------------------
                                   James C. Flores
                                   Chairman of the Board and
                                   Chief Executive Officer