<PAGE>
 
                            Titan Exploration, Inc.

                                  Exhibit 10
                                  ----------



Third Amendment to Amended and Restated Credit Agreement, dated May 12, 1997,
among Titan Resources, L.P., the Chase Manhattan Bank, as Administrative Agent
and Financial Institutions now or thereafter parties thereto.
<PAGE>
 
                                                                       EXHIBIT A

                        THIRD AMENDMENT TO AMENDED AND
                           RESTATED CREDIT AGREEMENT

                                 BY AND AMONG

                            TITAN RESOURCES, L.P.,
                                  as Company,


                           THE CHASE MANHATTAN BANK,
                           as Administrative Agent,


                          FIRST UNION NATIONAL BANK,
                            as Documentation Agent


                  MORGAN GUARANTY TRUST COMPANY OF NEW YORK,
                             as Syndication Agent,
 
                                      and

                         THE LENDERS SIGNATORY HERETO



                               December 12, 1997
<PAGE>
 
                        THIRD AMENDMENT TO AMENDED AND
                          RESTATED CREDIT AGREEMENT
                          -------------------------


     This THIRD AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT (this "Third
                                                                          -----
Amendment") dated effective as of the 12th day of December, 1997 (the "Effective
---------                                                              ---------
Date"), is by and among TITAN RESOURCES, L.P., a Texas limited partnership (the
----                                                                           
("Company"); THE CHASE MANHATTAN BANK, individually, as the Issuing Bank and as
  -------                                                                      
Administrative Agent (in such capacity, the "Administrative Agent"); FIRST UNION
                                             --------------------               
NATIONAL BANK, individually and as Documentation Agent (in such capacity, the
                                                                             
"Documentation Agent"); MORGAN GUARANTY TRUST COMPANY OF NEW YORK, individually
--------------------                                                           
and as Syndication Agent (in such capacity, the "Syndication Agent"); and each
                                                 -----------------            
of the lenders that is a signatory hereto or which becomes a signatory hereto
and to the Credit Agreement (hereinafter defined) as provided in Section 8.07 of
the Credit Agreement (individually, together with its successors and assigns,
                                                                             
"Lender" and collectively, "Lenders").
-------                     -------   

                             W I T N E S S E T H:
                             ------------------- 

     WHEREAS, the Company, the Administrative Agent, the Documentation Agent,
the Syndication Agent and Lenders are parties to that certain Amended and
Restated Credit Agreement dated as of October 31, 1996 (as amended by First
Amendment to Amended and Restated Credit Agreement dated as of May 12, 1997, and
as further amended by Second Amendment to Amended and Restated Credit Agreement
dated August 12, 1997, effective as of April 1, 1997, the "Credit Agreement"),
                                                           ----------------   
pursuant to which Lenders agreed to make loans to and extensions of credit on
behalf of the Company; and

     WHEREAS, the Company has requested and, subject to the terms and conditions
contained herein, the Administrative Agent, the Documentation Agent, the
Syndication Agent and Lenders have agreed to amend certain aspects of the Credit
Agreement to, among other things (a) permit the Company to make a $7,000,000
capital distribution to its limited partner, Titan Resources Holdings, Inc. and
(b) permit the Company to make a one-time advance to OEDC Exploration &
Production, L.P. using proceeds of a Loan hereunder to allow OEDC Exploration &
Production, L.P. to pay down certain outstanding indebtedness to Union Bank of
California, N.A.; and

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
herein contained, the parties hereto agree as follows:


                            ARTICLE I.  DEFINITIONS
                                        -----------
 
     Section 1.01  Terms Defined Above.  As used in this Third Amendment, each
                   -------------------                                          
of the terms "Administrative Agent," "Company," "Credit Agreement,"
              --------------------    -------    ----------------  
"Documentation Agent," "Lender," "Lenders," "Syndication Agent" and "Third
--------------------    ------    --------   -----------------       -----
Amendment" shall have the meaning assigned to such term hereinabove.
---------                                                           
<PAGE>
 
     Section 1.02  Terms Defined in Credit Agreement.  Each term defined in
                   ---------------------------------                         
the Credit Agreement and used herein without definition shall have the meaning
assigned to such term in the Credit Agreement, unless expressly provided to the
contrary.

     Section 1.03  Other Definitional Provisions.
                   -----------------------------   

          (a) The words "hereby," "herein," "hereinafter," "hereof," "hereto"
     and "hereunder" when used in this Third Amendment shall refer to this Third
     Amendment as a whole and not to any particular Article, Section, subsection
     or provision of this Third Amendment.

          (b) Section, subsection and Exhibit references herein are to such
     Sections, subsections and Exhibits to this Third Amendment unless otherwise
     specified.

                  ARTICLE II.  AMENDMENTS TO CREDIT AGREEMENT
                               ------------------------------
 
     The Company, the Administrative Agent, the Documentation Agent, the
Syndication Agent and Lenders agree that the Credit Agreement is hereby amended,
effective as of the Effective Date, in the following particulars.

     Section 2.01  Amendments and Supplements to Definitions.
                   -----------------------------------------   

          (a) The term "Agreement," as defined in the Credit Agreement, is
                        ---------                                         
     hereby amended to mean the Credit Agreement, as amended and supplemented by
     this Third Amendment and as the same may from time to time be further
     amended or supplemented.

          (b) The term "Guarantors," as defined in the Credit Agreement, is
                        ----------                                         
     hereby amended in its entirety to read as follows:

               "Guarantors" means (a) the Parent, (b) the General Partner, (c)
                ----------                                                    
          Titan Resources Holdings, Inc., a Nevada corporation, (d) OEDC E&P (e)
          Carrollton Resources, L.L.C., a Louisiana limited liability company,
          and (f) those Subsidiaries of the Parent or the Company designated as
          Guarantors on Exhibit B and any other Subsidiary of the Parent or the
                        ---------                                              
          Company, designated as a Guarantor by (i) the Company with the
          approval of the Administrative Agent, or (ii) the Majority Lenders, in
          each case pursuant to Section 5.01(j).

          (c) The terms "Subsidiary" or "Subsidiaries", as used in Sections 4.01
     through 4.05, Sections 4.07 through 4.18, Sections 4.20 through 4.23,
     Sections 5.01(a), (b), (c), (e), (f), (g), (h), (i), (k) and (l), Sections
     5.02 (f) and (j), and Sections 5.03(a), (b), (c), (e), (f), (g), (h), (j),
     (k) and (l), are hereby amended to include OEDC E&P.

                                      -2-
<PAGE>
 
     Section 2.02  New Definitions.  Section 1.01 of the Credit Agreement is
                   ---------------                                          
hereby amended and supplemented by adding thereto the following new definitions,
to read in their entirety as follows:

     "OEDC" means Offshore Energy Development Corporation, a Delaware
      ----                                                           
corporation, a wholly-owned subsidiary of the Parent.

     "OEDC E&P" means OEDC Exploration & Production, L.P., a Texas limited
      --------                                                            
partnership, the general partner of which is OEDC, Inc., a wholly-owned
subsidiary of OEDC.

     Section 2.03  Amendments to Section 5.02 - Reporting Covenants.
                   ------------------------------------------------ 

          (a) Sections 5.02 (a) and (b) of the Credit Agreement are hereby
     amended by (i) replacing the word "Company" with the word "Parent" in all
     places, and (ii) by replacing the word "Company's" with the word "Parent's"
     in all places.

          (b) Section 5.02 (d) is hereby amended by replacing the word "Company"
     with the words "Company and/or Parent" in all places.

     Section 2.04  Amendments to Section 5.03(a) B Indebtedness.  Section
                   --------------------------------------------          
5.03(a) of the Credit Agreement is hereby amended as follows:

          (a) Section 5.03(a)(iv) is hereby amended by deleting the word "and"
     following the "semi-colon (;)" at the end thereof.

          (b) Section 5.03(a)(v) is hereby amended by deleting the "period (.)"
     from the end thereof and substituting "; and" therefor.

          (c) Section 5.03(a) is hereby further amended by adding a new clause,
     to be clause (vi), to read in its entirety as follows:

          "(vi)  Indebtedness of any Guarantor permitted by Section 5.03(e)(x)
     hereof."

     Section 2.05  Amendment to Section 5.03(d) B Distribution, Etc.  Section
                   ------------------------------------------------          
5.03(d) of the Credit Agreement is hereby amended in its entirety to read as
follows:

          "(d)  Distribution, etc.  Make any distribution of profits or
                -----------------                                      
     purchase, redeem or otherwise acquire for value any of the partnership
     interests in the Company now or hereafter outstanding, return any capital
     to its Partners, or make any distribution of its assets to its Partners as
     such; provided, however, so long as no Default or Event of Default has
           --------  -------                                               
     occurred and is continuing hereunder or would occur as a consequence
     thereof, the Company may make (i) distributions to its Partners for the
     payment of cash taxes due and payable by the Partners as a result of their
     partnership interests in the Company, (ii) distributions to the Parent
     which will be used by the Parent from time to time to purchase up to and
     including $25,000,000 in the aggregate of its issued and outstanding common
     stock; provided,
            --------  

                                      -3-
<PAGE>
 
     however, no such distribution shall be made unless twenty-five percent
     -------
     (25%) of the Maximum Available Amount shall remain available under this
     Agreement after giving effect to the latest borrowings hereunder made in
     connection with the acquisition of the Parent's common stock, (iii) other
     distributions to its Partners not to exceed $2,500,000 in the aggregate in
     any calendar year, less the aggregate principal amount of Indebtedness
     permitted by Section 5.03(a)(v) which is incurred and outstanding in the
     same calendar year; and (iv) make, on or before November __, 1997, a
     one-time capital distribution to Titan Resources Holdings, Inc. in an
     amount not to exceed $7,000,000."

     Section 2.06  Amendment to Section 5.03(e) B Investments, Loans, etc.
                   ------------------------------------------------------  
Section 5.03(e)(x) of the Credit Agreement is hereby amended in its entirety to
read as follows:

          "(x)  unsecured intercompany loans permitted by Section 5.03(a)(v)
     hereof, and unsecured intercompany loans to any Guarantor which has
     executed and delivered a Guaranty Agreement in favor of the Administrative
     Agent for the benefit of the Lenders."

     Section 2.07  Amendment to Section 5.03(j) - Proceeds of Loans.  The
                   ------------------------------------------------      
first sentence of Section 5.03(j) of the Credit Agreement is hereby amended in
its entirety to read as follows:

     "Use any proceeds of the Loans for any purpose other than (i) to renew,
     rearrange and modify the outstanding principal balance owing under the
     Prior Notes, (ii) to acquire proven oil and gas properties, and development
     of oil and gas properties, (iii) for general corporate purposes, and (iv) a
     one-time advance to OEDC E&P of up to $30,000,000 to allow OEDC E&P to pay
     down certain outstanding balances owing to Union Bank of California, N.A.
     under or in connection with that certain First Restated Credit Agreement
     dated as of November 7, 1997 by and between OEDC E&P and Union Bank of
     California, N.A., in exchange for OEDC E&P's execution of a Guaranty
     Agreement guaranteeing prompt payment of the Lender Indebtedness."

                      ARTICLE III.  CONDITIONS PRECEDENT
                                    --------------------

     The obligation of the Administrative Agent, the Documentation Agent, the
Syndication Agent and each Lender to enter into this Third Amendment is subject
to the satisfaction of the following conditions:

     Section 3.01  Additional Documents.  The Administrative Agent shall have
                   --------------------                                      
received the following, each dated as of the Effective Date, in form and
substance satisfactory to the Administrative Agent, with an original thereof for
the Administrative Agent and with sufficient copies thereof for each Lender:

     (a) Guaranty Agreements.  A duly completed and executed Guaranty Agreement
         -------------------                                                   
from each of OEDC  E&P and Carrollton Resources, L.L.C., a Louisiana limited
liability company.

     (b) Security Instruments.  The instruments or documents described on
         --------------------                                            
Exhibit A attached to this Third Amendment, duly completed and executed by OEDC
---------                                                                      
E&P in a sufficient number of

                                      -4-
<PAGE>
 
counterparts for recording, if necessary, granting to the Administrative Agent,
for the benefit of the Lenders, first priority Liens (subject only to Liens
permitted under Section 5.03(b) of the Credit Agreement) upon certain Property
of OEDC E&P more particularly described therein as security for the payment and
performance of OEDC E&P's obligations under its Guaranty Agreement.

     (c) Other Documents.  Such other documents as the Administrative Agent or
         ---------------                                                      
any Lender or special counsel to the Administrative Agent may reasonably
request, all in form and substance satisfactory to the Administrative Agent.

     Section 3.02  Default or Event of Default.  There shall exist no Default or
                   ---------------------------                                  
no Event of Default under the Credit Agreement or any other Financing Document.

                          ARTICLE IV.  MISCELLANEOUS
                                       -------------
 
     Section 4.01  Adoption, Ratification and Confirmation of Credit Agreement.
                   -----------------------------------------------------------
Each of the Company, the Administrative Agent, the Documentation Agent, the
Syndication Agent and Lenders does hereby adopt, ratify and confirm the Credit
Agreement, as amended hereby, and acknowledges and agrees that the Credit
Agreement, as amended hereby, is and remains in full force and effect.

     Section 4.02  Successors and Assigns.  This Third Amendment shall be 
                   ----------------------                                  
binding upon and inure to the benefit of the parties hereto and their respective
successors and assigns permitted pursuant to the Credit Agreement.

     Section 4.03  Counterparts.  This Third Amendment may be executed by one or
                   ------------                                                
more of the parties hereto in any number of separate counterparts, and all of
such counterparts taken together shall be deemed to constitute one and the same
instrument and shall be enforceable as of the Effective Date upon the execution
of one or more counterparts hereof by the Company, the Administrative Agent, the
Documentation Agent, the Syndication Agent and Lenders. In this regard, each of
the parties hereto acknowledges that a counterpart of this Third Amendment
containing a set of counterpart execution pages reflecting the execution of each
party hereto shall be sufficient to reflect the execution of this Third
Amendment by each necessary party hereto and shall constitute one instrument.

     Section 4.04  Number and Gender.  Whenever the context requires, reference
                   -----------------                                   
herein made to the single number shall be understood to include the plural; and
likewise, the plural shall be understood to include the singular. Words denoting
sex shall be construed to include the masculine, feminine and neuter, when such
construction is appropriate; and specific enumeration shall not exclude the
general but shall be construed as cumulative. Definitions of terms defined in
the singular or plural shall be equally applicable to the plural or singular, as
the case may be, unless otherwise indicated.

     Section 4.05  Entire Agreement.  This Third Amendment constitutes the 
                   ----------------                                         
entire agreement among the parties hereto with respect to the subject hereof.
All prior understandings, statements and agreements, whether written or oral,
relating to the subject hereof are superseded by this Third Amendment.

                                      -5-
<PAGE>
 
     Section 4.06  Invalidity.  In the event that any one or more of the
                   ----------                                             
provisions contained in this Third Amendment shall for any reason be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality or
unenforceability shall not affect any other provision of this Third Amendment.

     Section 4.07  Titles of Articles, Sections and Subsections.  All titles
                   --------------------------------------------               
or headings to Articles, Sections, subsections or other divisions of this Third
Amendment or the exhibits hereto, if any, are only for the convenience of the
parties and shall not be construed to have any effect or meaning with respect to
the other content of such Articles, Sections, subsections, other divisions or
exhibits, such other content being controlling as the agreement among the
parties hereto.

     Section 4.08  Governing Law.  This Third Amendment shall be deemed to be
                   -------------                                               
a contract made under and shall be governed by and construed in accordance with
the internal laws of the State of New York.

     THIS THIRD AMENDMENT, THE CREDIT AGREEMENT, AS SUPPLEMENTED AND AMENDED
     HEREBY, THE NOTES, AND THE OTHER SECURITY INSTRUMENTS REPRESENT 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.

                                      -6-
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this Third Amendment to
be duly executed and delivered by their proper and duly authorized officers as
of the Effective Date.

BORROWER:                     TITAN RESOURCES, L.P., a Texas limited
--------                            partnership

                              By:  Titan Resources I, Inc., its General Partner


                                    By: /s/ Jack Hightower
                                       -------------------
                                    Name:  Jack Hightower
                                    Title: President


AGENT AND LENDERS:            THE CHASE MANHATTAN BANK, Individually as
-----------------             Issuing Bank and as Administrative Agent


                              By: /s/ Peter M. Ling
                                 ------------------
                              Name: Peter M. Ling
                              Title: Vice President


                              FIRST UNION NATIONAL BANK, Individually and
                              as Documentation Agent


                              By: /s/ Jay Chernowski
                                 -------------------
                              Name: Jay Chernowski
                              Title: Senior Vice President


                              MORGAN GUARANTY TRUST COMPANY OF
                              NEW YORK, Individually and as Syndication Agent


                              By: /s/ John Kowalozuk
                                 -------------------
                              Name: John Kowalozuk
                              Title: Vice President

                                      -7-
<PAGE>
 
                              CREDIT LYONNAIS NEW YORK BRANCH


                              By: /s/ Philipe Sousira
                                 --------------------
                              Name: Philippe Sousira
                              Title: Senior Vice President


                              BANK ONE, TEXAS, N.A.


                              By: /s/ Wm. Mark Cramer
                                 --------------------
                              Name: Wm. Mark Cramer
                              Title: Vice President


                              BANQUE PARIBAS


                              By: /s/ Brian M. Malone
                                 --------------------
                              Name: Brian M. Malone
                              Title: Director


                              By: /s/ Michael H. Fiuzat
                                 ----------------------
                              Name: Michael H. Fiuzat
                              Title: Vice President


                              UNION BANK OF CALIFORNIA, N.A.


                              By: /s/ Randal Osterberg
                                 ---------------------
                              Name: Randal Osterberg
                              Title: Vice President


                              By: /s/ Gary Shekerjian
                                 --------------------
                              Name: Gary Shekerjian
                              Title: Assistant Vice President

                                      -8-