<PAGE>
 
                                                                 EXHIBIT 10.13.3



                        SECOND 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 OF NORTH CAROLINA,
                            as Documentation Agent



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



                         THE LENDERS SIGNATORY HERETO



                            Dated August 12, 1997,
                         Effective as of April 1, 1997



<PAGE>
 
                              SECOND AMENDMENT TO
                     AMENDED AND RESTATED CREDIT AGREEMENT



     This SECOND AMENDMENT TO AMENDED AND RESTATED CREDIT AGREEMENT (this
"Second Amendment") dated August 12, 1997, effective, however, as of the 1st day
of April, 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 OF NORTH CAROLINA,
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, 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, the Administrative Agent, the Documentation Agent,
the Syndication Agent and Lenders desire to amend the Current Ratio covenant
contained in Section 5.03(o) of the Credit Agreement in the particulars
hereinafter provided;



     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 Second Amendment, each
of the terms "Administrative Agent," "Company," "Credit Agreement,"
"Documentation Agent," "Lender," "Lenders," "Second Amendment," and "Syndication
Agent" shall have the meaning assigned to such term hereinabove.



     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 Second Amendment shall refer to this
     Second Amendment as a whole and not to any particular Article, Section,
     subsection or provision of this Second Amendment.



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


<PAGE>
 
                  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 to Definitions.  The term "Agreement," as defined
in the Credit Agreement, is hereby amended to mean the Credit Agreement, as
amended and supplemented by this Second Amendment and as the same may from time
to time be further amended or supplemented.



     Section 2.02  Amendment to Section 5.03(o) Current Ratio.  Section 5.03(o)
of the Credit Agreement is hereby amended in its entirety to read as follows:



          "(o)  Current Ratio.  The Company will not permit its ratio of (i)
     consolidated current assets to (ii) consolidated current liabilities
     (excluding current maturities of the Notes) to be less than 1.0 to 1.0 at
     any time.  As used in this Section 5.03(o) "current assets" shall mean the
     aggregate of (i) all assets of a Person which under GAAP would be
     classified as current assets, and (ii) the Designated Borrowing Base, less
     the Aggregate Credit Exposure, and "current liabilities" shall mean all
     liabilities of a Person which under GAAP would be classified as current
     liabilities."



                          ARTICLE III.  MISCELLANEOUS



     Section 3.01  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 3.02  Successors and Assigns.  This Second 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 3.03  Counterparts.  This Second 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 Second Amendment
containing a set of counterpart execution pages reflecting the execution of each
party hereto shall be sufficient to reflect the execution of this Second
Amendment by each necessary party hereto and shall constitute one instrument.



     Section 3.04  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 3.05  Entire Agreement.  This Second 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 Second Amendment.



     Section 3.06  Invalidity.  In the event that any one or more of the
provisions contained in this Second 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 Second Amendment.


<PAGE>
 
     Section 3.07  Titles of Articles, Sections and Subsections.  All titles or
headings to Articles, Sections, subsections or other divisions of this Second
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 3.08  Governing Law.  This Second 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 Second 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.


     IN WITNESS WHEREOF, the parties hereto have caused this Second 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, CEO
                                          -------------------------



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



                              By: /s/ Mary Jo Woodford
                                 ----------------------------------
                              Name: Mary Jo Woodford
                                   --------------------------------
                              Title: Vice President
                                    -------------------------------



                              FIRST UNION NATIONAL BANK,  Individualy and as
                              Documentation Agent



                              By: /s/ Michael J. Kolosowsky
                                 ----------------------------------
                              Name: Michael J. Kolosowsky
                                   --------------------------------
                              Title: Vice President
                                    -------------------------------

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



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



                              CREDIT LYONNAIS NEW YORK BRANCH



                              By: /s/ Pascal Poupelle
                                 ---------------------------
                              Name: Pascal Poupelle
                                  --------------------------
                              Title: Executive Vice President
                                  --------------------------
                              


                              BANK ONE, TEXAS, N.A.



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


                              BANQUE PARIBAS



                              By: /s/ Brian Malone
                                 ---------------------------
                              Name: Brian Malone
                                  --------------------------
                              Title: Vice President
                                  --------------------------
                              



                              By: /s/ Barton D. Schouest
                                 ---------------------------
                              Name: Barton D. Schouest
                                   -------------------------
                              Title: Managing Director
                                   -------------------------



                              UNION BANK OF CALIFORNIA, N.A.



                              By: /s/ Tony R. Weber
                                 ---------------------------
                              Name: Tony R. Weber
                                  --------------------------
                              Title: Vice President
                                   -------------------------



                              By: /s/ Randall Osterbert
                                 ---------------------------
                              Name: Randall Osterbert
                                   -------------------------
                              Title: Vice President
                                   -------------------------