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                                                                     EXHIBIT 3.4

                               SECOND AMENDMENT TO

                                     BYLAWS

                                       OF

                           EDGE PETROLEUM CORPORATION


The following amendment to the Bylaws was adopted by the Board of Directors of
Edge Petroleum Corporation (the "Corporation") on May 7, 2003:

          Section 2.8(a) of the Bylaws of the Corporation is hereby amended and
restated in its entirety to read as follows:

          (a) At an annual meeting of stockholders, only such business shall be
     conducted, and only such proposals shall be acted upon, as shall have been
     brought before the annual meeting (i) by or at the direction of the Board
     of Directors or (ii) by any stockholder of the Corporation who is a
     stockholder of record at the time of the giving of such stockholder's
     notice provided for in this Section 2.8, who shall be entitled to vote at
     such meeting and who complies with the requirements of this Section 2.8 and
     as shall otherwise be proper subjects for stockholder action and shall be
     properly introduced at the meeting. For a proposal to be properly brought
     before an annual meeting by a stockholder, in addition to any other
     applicable requirements, the stockholder must have given timely advance
     notice thereof in writing to the Secretary of the Corporation. To be
     timely, a stockholder's notice must be delivered to, or mailed and received
     at, the principal executive offices of the Corporation not later than the
     close of business on the 120th day prior to the first anniversary of the
     preceding year's annual meeting; provided, however, that in the event that
     the date of the annual meeting is more than 30 days before or more than 60
     days after such anniversary date, notice by the stockholder to be timely
     must be so delivered not later than the close of business on the later of
     the 120th day prior to such annual meeting or the 10th day following the
     day on which public announcement of the date of such meeting is first made
     by the Corporation. Any such stockholder's notice to the Secretary of the
     Corporation shall set forth as to each matter the stockholder proposes to
     bring before the annual meeting (i) a description of the proposal desired
     to be brought before the annual meeting and the reasons for conducting such
     business at the annual meeting, (ii) the name and address, as they appear
     on the Corporation's books, of the stockholder proposing such business and
     any other stockholders known by such stockholder to be supporting such
     proposal, (iii) the class and number of shares of the Corporation's stock
     that are beneficially owned by the stockholder on the date of such notice,
     (iv) any financial interest of the stockholder in such proposal and (v) a
     representation that the stockholder intends to appear in person or by proxy
     at the meeting to bring the proposed business before the annual meeting.
     The presiding officer of the annual meeting shall determine whether the
     requirements of this paragraph (a) have been met with respect to any
     stockholder proposal. If the presiding officer determines that a
     stockholder proposal was not made in accordance with the terms of this
     paragraph (a), he shall so declare at the meeting and any such proposal
     shall not be acted upon at the meeting. At a special meeting of
     stockholders, only such business shall be acted upon as


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     shall have been set forth in the notice relating to the meeting required by
     Section 2.4 hereof or as shall constitute matters incident to the conduct
     of the meeting as the presiding officer of the meeting shall determine to
     be appropriate.

          Section 3.3 of the Bylaws of the Corporation is hereby amended and
restated in its entirety to read as follows:

          Nomination of Directors. Subject to such rights of the holders of one
     or more outstanding series of Preferred Stock of the Corporation to elect
     one or more directors in case of arrearages in the payment of dividends or
     other defaults as shall be prescribed in the Certificate of Incorporation
     or in the resolutions of the Board of Directors providing for the
     establishment of any such series, only persons who are nominated in
     accordance with the procedures set forth in this Section 3.3 shall be
     eligible for election as, and to serve as, directors. Nominations of
     persons for election to the Board of Directors may be made at a meeting of
     the stockholders at which Directors are to be elected (i) by or at the
     direction of the Board of Directors or (ii) by any stockholder of the
     Corporation who is a stockholder of record at the time of the giving of
     such stockholder's notice provided for in this Section 3.3, who shall be
     entitled to vote at such meeting in the election of directors and who
     complies with the requirements of this Section 3.3. Such nominations, other
     than those made by or at the direction of the Board of Directors, shall be
     preceded by timely advance notice in writing to the Secretary of the
     Corporation. To be timely, a stockholder's notice shall be delivered to, or
     mailed and received at, the principal executive offices of the Corporation
     (i) with respect to an election to be held at the annual meeting of the
     stockholders of the Corporation, not later than the close of business on
     the 120th day prior to the first anniversary of the preceding year's annual
     meeting; provided, however, that in the event that the date of the annual
     meeting is more than 30 days before or more than 60 days after such
     anniversary date, notice by the stockholder to be timely must be so
     delivered not later than the close of business on the later of the 120th
     day prior to such annual meeting or the 10th day following the day on which
     public announcement of the date of such meeting is first made by the
     Corporation; and (ii) with respect to an election to be held at a special
     meeting of stockholders of the Corporation for the election of directors
     not later than the close of business on the tenth day following the day on
     which notice of the date of the special meeting was mailed to stockholders
     of the Corporation as provided in Section 2.4 hereof or public disclosure
     of the date of the special meeting was made, whichever first occurs. Any
     such stockholder's notice to the Secretary of the Corporation shall set
     forth (x) as to each person whom the stockholder proposes to nominate for
     election or re-election as a director, (i) the name, age, business address
     and residence address of such person, (ii) the principal occupation or
     employment of such person, (iii) the number of shares of each class of
     capital stock of the Corporation beneficially owned by such person, (iv)
     the written consent of such person to having such person's name placed in
     nomination at the meeting and to serve as a director if elected and (v) any
     other information relating to such person that is required to be disclosed
     in solicitations of proxies for election of directors, or is otherwise
     required, pursuant to Regulation 14A under the Exchange Act, and (y) as to
     the stockholder giving the notice, (i) the name and address, as they appear
     on the Corporation's books, of such stockholder and (ii) the number of
     shares of each class of voting stock of the Corporation that are then
     beneficially owned by such stockholder. The presiding officer of the


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     meeting of stockholders shall determine whether the requirements of this
     Section 3.3 have been met with respect to any nomination or intended
     nomination. If the presiding officer determines that any nomination was not
     made in accordance with the requirements of this Section 3.3, he shall so
     declare at the meeting and the defective nomination shall be disregarded.
     Notwithstanding the foregoing provisions of this Section 3.3, a stockholder
     shall also comply with all applicable requirements of the Exchange Act and
     the rules and regulations thereunder with respect to the matters set forth
     in this Section 3.3.


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