<PAGE>   1
                                                                   EXHIBIT 10.29


            FIRST AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT


         THIS FIRST AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT (this
"First Amendment") is made and entered into as of the 31st day of December,
1999, by and among MARINER ENERGY, INC., a Delaware corporation ("Borrower"),
BANK OF AMERICA, N.A., as Administrative Agent ("Administrative Agent"), TORONTO
DOMINION (TEXAS), INC., as Co-Agent ("Co-Agent") and BANK OF AMERICA, N.A.,
TORONTO DOMINION (TEXAS), INC., THE BANK OF NOVA SCOTIA and ABN AMRO BANK N.V.
(individually a "Bank" and collectively the "Banks").

         WHEREAS, Borrower, NationsBank, N.A. (which changed its name to Bank of
America, N.A., and then merged with and into Bank of America National Trust and
Savings Association, which surviving entity then changed its name to Bank of
America, N.A.), as Administrative Agent, Co-Agent and the Banks entered into
that certain Amended and Restated Credit Agreement dated June 28, 1999 (the
"Credit Agreement");

         WHEREAS, Borrower, Administrative Agent, Co-Agent and the Banks desire
to amend certain terms and provisions of the Credit Agreement, as set forth
herein.

         NOW, THEREFORE, FOR AND IN CONSIDERATION of the mutual covenants and
agreements contained herein, the parties hereto agree as follows:

     1. Section 10.2 of the Credit Agreement is deleted in its entirety, and the
following is substituted in its place:

                  Section 10.2. Interest Coverage Ratio. Borrower will not
         permit the consolidated Interest Coverage Ratio of Borrower and
         Guarantor as of the end of the Fiscal Quarter ending December 31, 1999
         to be less than 2.00 to 1.0. Borrower will not permit the consolidated
         Interest Coverage Ratio of Borrower and Guarantor as of the end of any
         other Fiscal Quarter to be less than 2.25 to 1.0.

     1. The closing of the transactions contemplated by this First Amendment is
subject to the satisfaction of the following conditions:

                  (a) All legal matters incident to the transactions herein
         contemplated shall be satisfactory to counsel to Administrative Agent;
         and

                  (b) Administrative Agent shall have received a fully executed
         copy of this First Amendment.

     1. Except as amended hereby, the Credit Agreement shall remain unchanged,
and the terms, conditions and covenants of the Credit Agreement shall continue
and be binding upon the parties hereto.

     1. Within thirty (30) days of the next action, whether by consent or at a
meeting, of the Board of Directors of Borrower and Guarantor, Borrower will
deliver an executed copy of resolutions



<PAGE>   2

of the Board of Directors of Borrower and Guarantor in form and substance
reasonably satisfactory to Administrative Agent ratifying the execution,
delivery and performance of this First Amendment and all documents, instruments
and certificates referred to herein.

     1. Each of the terms defined in the Credit Agreement is used in this First
Amendment with the same meaning, except as otherwise indicated in this First
Amendment. Each of the terms defined in this First Amendment is used in the
Credit Agreement with the same meaning, except as otherwise indicated in the
Credit Agreement.

     1. This First Amendment may be executed in any number of counterparts, each
of which shall constitute an original, but all of which, when taken together,
shall constitute but one agreement.

     1. THIS FIRST AMENDMENT SHALL BE DEEMED TO BE A CONTRACT UNDER, SUBJECT TO,
AND SHALL BE CONSTRUED FOR ALL PURPOSES IN ACCORDANCE WITH THE LAWS OF THE STATE
OF TEXAS.

     1. THE CREDIT AGREEMENT, AS AMENDED, REPRESENTS THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR
SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES.

         THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

     IN WITNESS WHEREOF, the parties have caused this First Amendment to be
executed by their duly authorized officers as of the day and year first above
written.


                                 MARINER ENERGY, INC.


                                 By:   /s/ Frank Pici
                                   Name:  Frank Pici
                                   Title: Vice President Finance


                                 BANK OF AMERICA, N.A., as Administrative Agent


                                 By:   /s/ James Ducoto
                                   Name:  James Ducoto
                                   Title: Vice President



                                 TORONTO DOMINION (TEXAS), INC.,
                                 as Co-Agent


                                 By:   /s/ Mark A. Bario
                                   Name:  Mark A. Bario
                                   Title: Vice President


-2-

<PAGE>   3





                                 BANK OF AMERICA, N.A.


                                 By:      /s/ Mark Barid
                                       Name:       Mark Barid
                                       Title:      Vice President


                                 TORONTO DOMINION (TEXAS), INC.


                                 By:      /s/ [ILLEGIBLE]
                                       Name:       [ILLEGIBLE]
                                       Title:      Vice President


                                 THE BANK OF NOVA SCOTIA


                                 By:      /s/ [ILLEGIBLE]
                                       Name:       [ILLEGIBLE]
                                       Title:      Vice President


                                 ABN AMRO BANK N.V.


                                 By:      /s/ Matt McCain
                                       Name:       Matt McCain
                                       Title:      Vice President


                                 By:      /s/ Deanna Breland
                                       Name:       Deanna Breland
                                       Title:      Vice President


         The undersigned Guarantor, Mariner Holdings, Inc., executes this First
Amendment to evidence its acknowledgment of the terms and provisions hereof and
to evidence its agreements to the matters set forth herein.

                                 MARINER HOLDINGS, INC.


                                 By:      /s/ Frank Pici
                                       Name:       Frank Pici
                                       Title:      Vice President - Finance




-3-