<PAGE>
                                                                     Exhibit 3.4


                                                          STATE OF DELAWARE
                                                          SECRETARY OF STATE
                                                       DIVISION OF CORPORATIONS
                                                      FILED 03:40 PM 05/16/2001
                                                          010235781 - 2383012


                             Certificate of Merger
                            Of Bargo Energy Company
                  With and into Bellwether Exploration Company

Pursuant to the provisions of Section 252 of the Delaware General Corporation
Law, the undersigned adopt the following Certificate of Merger for the purpose
of merging them into one of such corporation and certify as follows:

1.   The name and state of incorporation of each corporation which is a party to
     the merger is:

                       Name                          State
                       ----                          -----

            Bellwether Exploration Company          Delaware
            Bargo Energy Company                     Texas

2.   The surviving corporation of the merger is Bellwether Exploration Company.

3.   The Agreement and Plan of Merger has been approved, adopted, certified,
     executed and acknowledged by the directors and shareholders of Bargo Energy
     Company and the directors and stockholders of Bellwether Exploration
     Company.

4.   The following amendment to the Certificate of Incorporation of the
     surviving corporation shall be effected in connection with the merger.

     Article One of the Certificate of Incorporation of the surviving
     corporation shall be deleted and replaced in its entirety as follows:

                                  "ARTICLE ONE

     The name of the corporation is Mission Resources Corporation."

5.   An executed copy of the Agreement and Plan of Merger is on file at the
     principal place of business of the surviving corporation, which place of
     business is located at Bellwether Exploration Company, 1331 Lamar, Suite
     1455, Houston, Texas 77010.

6.   A copy of the Agreement and Plan of Merger will be furnished by the
     surviving corporation on written request and without cost to the
     shareholders of Bargo Energy Company and the stockholders of Bellwether
     Exploration Company.

7.   As to Bargo Energy Company, the Texas corporation, the Agreement and Plan
     of Merger was duly authorized and approved by all action required by the
     laws of the State of Texas and by its constituent documents.

8.   As to Bellwether Exploration Company, the Delaware corporation, the
     Agreement and Plan of Merger was duly authorized and approved by all action
     required by the laws of the State of Delaware and by its constituent
     documents. The total number of shares outstanding, voted for and against
     the Agreement and Plan of Merger, and as to each class entitled to vote
     thereon as a class, the number of shares voted for and against the
     Agreement and Plan of Merger:

<PAGE>

<TABLE>
<CAPTION>

                                                                 Entitled to Vote as a Class
                                                              ---------------------------------
                                        Total       Total
                           Total        Voted       Voted              Total    Voted    Voted
Name of Corporation       Shares         For       Against    Class    Shares    For    Against
-------------------       ------        -----      -------    -----    ------   ------  -------
<S>                      <C>           <C>         <C>        <C>      <C>      <C>      <C>
Bellwether Exploration   14,046,233    7,139,306   68,725      N/A      N/A      N/A      N/A
Company
</TABLE>

9.   The surviving corporation will be responsible for the payment of all fees
     and franchise taxes and will be obligated to pay such fees and franchise
     taxes if the same are not timely paid.

     IN WITNESS WHEREOF, these Certificate of Merger have been duly executed and
delivered on this 16th day of May, 2001.


                                   BELLWETHER EXPLORATION COMPANY



                                   /s/ Douglas G. Manner
                                   --------------------------------------------
                                   Name:  Douglas G. Manner
                                   Title: Chief Executive Officer and President



                                   BARGO ENERGY COMPANY



                                   /s/ Jonathan M. Clarkson
                                   --------------------------------------------
                                   Name:  Jonathan M. Clarkson
                                   Title: President and Chief Operating Officer