<PAGE>

                                                                 EXHIBIT 10.4.2

                              SECOND AMENDMENT TO
                  SECOND AMENDED AND RESTATED CREDIT AGREEMENT


                           dated as of July 18, 2001


                                     among


                     SPINNAKER EXPLORATION COMPANY, L.L.C.,
                                  AS BORROWER

                                      and

                        CERTAIN FINANCIAL INSTITUTIONS,
                                  AS LENDERS,

                        TORONTO DOMINION (TEXAS), INC.,
                            AS ADMINISTRATIVE AGENT,

                                      and

                          CREDIT SUISSE FIRST BOSTON,
                             AS DOCUMENTATION AGENT
<PAGE>

                              SECOND AMENDMENT TO
                  SECOND AMENDED AND RESTATED CREDIT AGREEMENT

     THIS SECOND AMENDMENT TO SECOND AMENDED AND RESTATED CREDIT AGREEMENT,
dated as of July 18, 2001 (this "Second Amendment"), is among SPINNAKER
EXPLORATION COMPANY, L.L.C., a Delaware limited liability company (the
"Borrower"), the commercial lending institutions parties hereto (the "Lenders"),
CREDIT SUISSE FIRST BOSTON, as documentation agent (in such capacity, the
"Documentation Agent") for the Lenders, and TORONTO DOMINION (TEXAS), INC., as
administrative agent (in such capacity together with its successors in such
capacity, the "Administrative Agent") for the Lenders.

                              W I T N E S S E T H:

     WHEREAS, Borrower, the Administrative Agent, the Documentation Agent, the
Issuer and the Lenders have heretofore entered into that certain Second Amended
and Restated Credit Agreement, dated as of July 20, 2000, as amended by that
certain First Amendment to Second Amended and Restated Credit Agreement dated
September 30, 2000 (as so amended and as may be amended, supplemented, restated
or otherwise modified from time to time, the "Credit Agreement"); and

     WHEREAS, Borrower, the Administrative Agent, the Documentation Agent, the
Issuer and the Lenders now intend to amend the Credit Agreement in certain
respects.

     NOW, THEREFORE, in consideration of the premises and of the mutual
covenants herein contained, each of Borrower, the Administrative Agent, the
Issuer and the Lenders agree as follows:

     SECTION 1. Defined Terms. Terms defined in the Credit Agreement are used in
this Second Amendment with the same meaning, unless otherwise indicated.

     SECTION 2. Amendments to Credit Agreement.

     A.   The definition of "Base Rate Spread" in Section 1.1 of the Credit
Agreement is hereby amended and restated in its entirety as follows:

          "Base Rate Spread" means, with respect to any Loan bearing interest at
     the Base Rate for any time prior to the Final Maturity Date, the applicable
     margin set forth below under the caption "Base Rate Spread", determined by
     reference to the percentage of the Borrowing Base that the sum of all Loans
     outstanding plus all LC Obligations represent at that time.

               Percentage of
              Borrowing Base
                  Usage                                     Base Rate Spread
           ------------------                              -----------------
greater than or equal to 75%                                    0.25%
greater than or equal to 60% but less than 75%                  0.00%
greater than 40% but less than 60%                              0.00%
less than or equal to 40%                                       0.00%
<PAGE>

     B. The definition of "Commitment Fee Rate" in Section 1.1 of the Credit
Agreement is hereby amended and restated in its entirety as follows:

          "Commitment Fee Rate" means for any time prior to the Conversion Date,
     a rate equal to the applicable margin set forth below under the caption
     "Commitment Fee Rate", determined by reference to the percentage of the
     Borrowing Base that the sum of all Loans outstanding plus all LC
     Obligations represent at that time.

                    Percentage of
                   Borrowing Base                          Commitment Fee
                      Usage                                     Rate
                  ------------------                      ---------------
greater than or equal to 75%                                    0.40%
greater than or equal to 60% but less than 75%                  0.35%
greater than 40% but less than 60%                              0.30%
less than or equal to 40%                                       0.25%

     C. The definition of "LIBOR Spread" in Section 1.1 of the Credit Agreement
is hereby amended and restated in its entirety as follows:

          "LIBOR Spread" means with respect to any Loan bearing interest at the
     LIBOR Rate for any time prior to the Final Maturity Date, the applicable
     margin set forth below under the caption "LIBOR Rate Spread," determined by
     reference to the percentage of the Borrowing Base that the sum of all Loans
     outstanding plus all LC Obligations represents at that time.

                   Percentage of
                  Borrowing Base                              LIBOR Rate
                      Usage                                     Spread
                 ------------------                          -----------
greater than or equal to 75%                                    1.75%
greater than or equal to 60% but less than 75%                  1.50%
greater than 40% but less than 60%                              1.25%
less than or equal to 40%                                       1.00%

                                       2
<PAGE>

     D. The definition of "Loan Documents" in Section 1.1 of the Credit
Agreement is hereby amended by deleting the words ", the Pledge Agreements".

     E. The definition of "Subject Hedging Agreements" in Section 1.1 of the
Credit Agreement is hereby amended by deleting the words "and secured by the
Security Documents".

     F. Clause (b) of Section 2.1(a) of the Credit Agreement is hereby amended
by deleting the words ", does not exceed such Lender's Percentage Share of the
Borrowing Base then outstanding" with the words ", does not exceed such Lender's
Percentage Share of the Borrowing Base plus such Lender's Percentage Share of
all Indebtedness incurred under Section 6.2(a)(vi) hereof then outstanding".

     G. Clause (c) of Section 2.1(a) of the Credit Agreement is hereby amended
and restated in its entirety as follows:

          "(c) the aggregate amount of all Revolving Loans outstanding plus all
     LC Obligations plus all Indebtedness incurred under Section 6.2(a)(vi)
     hereof does not exceed the Borrowing Base then outstanding."

     H. Section 2.10(b)(i) of the Credit Agreement is hereby amended as follows:

          (i) by replacing the words "If at any time the aggregate unpaid
     principal balance of the Loans plus the aggregate amount of LC Obligations
     exceeds the Borrowing Base" with the words "If at any time the aggregate
     unpaid principal balance of the Loans plus the aggregate amount of LC
     Obligations plus the aggregate Indebtedness incurred under Section
     6.2(a)(vi) hereof exceeds the Borrowing Base";

          (ii) by replacing the words "three (3) (or fewer) monthly
     installments" with the words "six (6) (or fewer) monthly installments" in
     clause (2) thereof; and

          (iii)  by replacing the reference to "one-third" with a reference to
     "one-sixth" in the last sentence thereof.

     I. Section 2.10(b)(ii) of the Credit Agreement is hereby amended by
replacing the reference to "100%" with a reference of "80%".

     J. Section 2.11(e) of the Credit Agreement is hereby amended by deleting
the words "secured by the Security Documents" and inserting the words "of any
Related Person" before the words "to Lenders".

     K. Section 2.13(b) of the Credit Agreement is hereby amended by replacing
the words "acquired from time to time as Collateral for the Obligations, which
may then" with the word "to" and replacing the language in clause (B) thereof
with "[intentionally omitted]".

                                      3
<PAGE>

     L.   Section 3.6(a) of the Credit Agreement is hereby amended by adding the
words "plus all Indebtedness permitted pursuant to Section 6.2(a)(vi) hereof"
before the words "will exceed the Borrowing Base".

     M.   Section 3.6(c) of the Credit Agreement is hereby amended by deleting
the words ", and Borrower agrees that such LC Collateral and investments shall
be subject to all of the terms and conditions of the Mortgage".

     N.   The second sentence of Section 5.1(f) of the Credit Agreement is
hereby deleted in its entirety.

     O.   Section 6.1(b)(iv) of the Credit Agreement is hereby amended by
replacing the words "an Engineering Report prepared by Borrower's in-house
engineering staff as of July 1 of such year" with the words "an Engineering
Report prepared by Borrower's in-house engineering staff or Ryder Scott Company
or any other independent engineer approved by Administrative Agent as of June 30
of such year".

     P.   Section 6.1(b)(viii) of the Credit Agreement is hereby amended by
replacing the words "calendar month" with the words "Fiscal Quarter".

     Q.   Section 6.1(d) of the Credit Agreement is hereby amended by (i) adding
the word "and" at the end of clause (vi) thereof following the comma; (ii)
deleting clause (vii) thereof in its entirety; (iii) renumbering clause (viii)
thereof as clause (vii), and (iv) replacing the word "Collateral" with the words
"properties and assets of Borrower and its Subsidiaries".

     R.   Section 6.1(e) of the Credit Agreement is hereby amended by replacing
the word "Collateral" with the words "properties and assets of Borrower and its
Subsidiaries".

     S.   Section 6.2(a) of the Credit Agreement is hereby amended by deleting
the "and" at the end of clause (iii) thereof, replacing the period at the end of
clause (iv) thereof with a semicolon and adding the following:

          "(v)  unsecured vendor Indebtedness of Borrower (but not of any of its
     Subsidiaries) related to purchases of 2-D and 3-D seismic data made in the
     ordinary course of business in an amount not to exceed $25,000,000 in the
     aggregate, except that such vendor Indebtedness may be secured by such 2-D
     and 3-D seismic data; and

          (vi) other unsecured Indebtedness of the Borrower or Spinnaker
     Exploration Company (but not of any of their respective Subsidiaries) in an
     amount not to exceed $10,000,000 in the aggregate, provided that
     contemporaneously with the incurrence of such Indebtedness, Borrower
     provides notice to Administrative Agent of the general terms of such
     Indebtedness and certifies to Administrative Agent as to the amount of such
     incurred Indebtedness, the aggregate amount of all Indebtedness incurred
     under this clause (vi) and the unsecured nature of such Indebtedness."

                                       4
<PAGE>

     T.   Section 6.2(d)(iii) of the Credit Agreement is hereby amended by (i)
replacing references to the amount "$500,000" with references to the amount
"$25,000,000" and (ii) amending and restating clause (2) thereof in its entirety
as follows:

          "(2) 80% of the Net Sales Proceeds therefrom shall be applied as set
     forth in Section 2.10(b)(ii)(A) and thereafter as set forth in Section
     2.10(b)(ii)(B)."

     U.   Section 6.2(e)(iii) of the Credit Agreement is hereby amended and
restated in its entirety as follows:

          "(iii) by Borrower to members of Borrower by way of distributions or
     dividends only, provided that such distributions or dividends either (A)
     are solely used directly or indirectly to pay either current taxes or
     employee compensation paid within the ordinary course of business
     (including bonuses and payments under employment contracts existing on the
     Closing Date) or (B) do not exceed $10,000,000 in the aggregate;"

     V.   Section 6.2(i) of the Credit Agreement is hereby amended by deleting
the words "or the PGS Data Contract".

     W.   Section 6.2(l) of the Credit Agreement is hereby amended by replacing
the number "5.00" with the number "3.00".

     X.   Section 6.2 of the Credit Agreement is hereby amended by adding a new
clause (o) at the end thereof as follows:

          "(o)  Negative Pledges, Restrictive Agreements, etc.  The Borrower
     will not, and will not permit any of its Subsidiaries to, enter into any
     agreement (excluding this Agreement, any other Loan Document and any
     agreement governing any Indebtedness permitted by Section 6.2(a)(iii) as to
     the assets financed with the proceeds of such Indebtedness) prohibiting

               (i) the creation or assumption of any Lien upon its properties,
          revenues or assets, whether now owned or hereafter acquired, or the
          ability of the Borrower or any other Related Person to amend or
          otherwise modify this Agreement or any other Loan Document; or

               (ii) the ability of any Subsidiary to make any payments, directly
          or indirectly, to the Borrower by way of dividends, advances,
          repayments of loans or advances, reimbursements of management and
          other intercompany charges, expenses and accruals or other returns on
          investments, or any other agreement or arrangement which restricts the
          ability of any such Subsidiary to make any payment, directly or
          indirectly, to the Borrower."

                                       5
<PAGE>

     Y.   The heading to Article VII of the Credit Agreement is hereby changed
to "Offset; Additional Subsidiaries".

     Z.   Sections 7.1, 7.2 and 7.3 of the Credit Agreement are hereby amended
and restated in its entirety as follows:

          "Section 7.1  [Intentionally Omitted].

          Section 7.2  [Intentionally Omitted].

          Section 7.3  [Intentionally Omitted]."

     AA.  Section 7.5 of the Credit Agreement is hereby amended and restated in
its entirety as follows:

          "Section 7.5  Additional Subsidiaries.  With five (5) Business Days
     after Borrower or any Subsidiary creates, acquires or otherwise forms a
     Subsidiary, Borrower shall: (a) cause such Subsidiary to execute and
     deliver to Administrative Agent on behalf of the Lenders a guaranty
     substantially similar to the guaranties executed and delivered on the
     Closing Date; (b) deliver or cause to be delivered to Administrative Agent
     on behalf of the Lenders all agreements, documents, instruments and other
     writings described in Section 4.1(c)(i), (d) and (k), with respect to such
     Subsidiary; and (c) deliver or cause to be delivered to Administrative
     Agent on behalf of the Lenders all such information regarding the condition
     (financial or otherwise), business and operations of such Subsidiary as
     Administrative Agent or any Lender through Administrative Agent may
     reasonably request."

     BB.  Section 7.6 of the Credit Agreement is hereby deleted in its entirety.

     CC.  Section 8.1(j) of the Credit Agreement is hereby amended and restated
in its entirety as follows:

          "(j)  [Intentionally omitted];"

     DD.  Section 8.1(l) of the Credit Agreement is hereby amended and restated
in its entirety as follows:

          "(l)  any of the Guaranties shall cease, for any reason, to be in full
     force and effect, or any Related Person or any Affiliate thereof shall so
     assert, and such shall not be remedied with fifteen (15) days after notice
     from Administrative Agent."

     EE.  Section 9.6 of the Credit Agreement is hereby amended by deleting the
words "rights under Security Documents or".

                                       6
<PAGE>

     FF.  Section 10.1(a) of the Credit Agreement is hereby amended by replacing
the words "Secured Hedging Agreements" with the words "Subject Hedging
Agreements" and by replacing the reference to "Collateral" with a reference to
"oil and gas properties".

     GG.  Exhibit J of the Credit Agreement is hereby amended by deleting the
words "as Collateral" at the end of the Exhibit.

     HH.  Sections 1, 2 and 3 of Schedule 2 to the Credit Agreement is hereby
amended and restated in its entirety as follows:

          "1.  Mortgages: None.
          2.   General Security Agreement: None.
          3.   Pledge and Security Agreement: None."

     II.  All references to "Mortgaged Property" in the Credit Agreement shall
be deemed to be references to "oil and gas property".  The definition of
"Mortgaged Property" is hereby deleted in its entirety.

     SECTION 3. New Conversion Date. The parties hereto acknowledge and agree
that, upon the effectiveness of this Second Amendment, the current Conversion
Date of July 19, 2001 shall be extended to a date that is 364 days from the date
hereof (the "New Conversion Date"). From and after the effectiveness of this
Second Amendment, each Lender hereby agrees that the effective Conversion Date
under the Credit Agreement shall be the New Conversion Date, as such date may be
extended in accordance with Section 2.2 of the Credit Agreement. The parties
hereto agree that the execution and delivery of this Second Amendment is in lieu
of the delivery of a Certificate of Extension under Section 2.2 of the Credit
Agreement for the purpose of extending the Conversion Date thereunder, and each
Lender further agrees to waive the delivery of such Certificate of Extension and
any accompanying notice requirements under Section 2.2 of the Credit Agreement
for the limited purpose of the extension of the current Conversion Date to the
New Conversion Date.

     SECTION 4. Conditions to Effectiveness. The effectiveness of this Second
Amendment shall be subject to the prior or concurrent satisfaction, on or before
July 18, 2001, of the conditions precedent that the Administrative Agent shall
have received all of the following, in form and substance satisfactory to the
Administrative Agent, and in sufficient number of signed counterparts to provide
one for each Lender:

     A.   Counterparts of this Second Amendment, duly executed by each of
Borrower, the Administrative Agent, the Documentation Agent, the Issuer and the
Majority Lenders; and

     B.   Such other documents as the Administrative Agent may reasonably
request.

     Upon satisfaction of the foregoing conditions precedent, this Second
Amendment shall be effective as of the date first above written.

                                       7
<PAGE>

     SECTION 5. Representations and Warranties. To induce the Lenders, the
Issuer, the Administrative Agent and the Documentation Agent to enter into this
Second Amendment, Borrower hereby reaffirms, as of the date hereof, its
representations and warranties contained in Article V of the Credit Agreement
(except to the extent such representations and warranties relate solely to an
earlier date, in which case such representations and warranties shall relate
solely to such earlier date) and additionally represents and warrants as
follows:

     A.   Authorization.  Borrower has duly taken all action necessary to
authorize the execution and delivery by it of this Second Amendment and to
authorize the consummation of the transactions contemplated thereby and the
performance of its obligations hereunder.

     B.   No Conflicts or Consents.  The execution and delivery by Borrower of
this Second Amendment, the performance by each of its obligations under this
Second Amendment, and the consummation of the transactions contemplated by this
Second Amendment, do not and will not (i) conflict with any provision of (1) any
domestic or foreign law, statute, rule or regulation, (2) the organizational
documents of Borrower, or (3) any agreement, judgment, license, order or permit
applicable to or binding upon Borrower, (ii) result in the acceleration of any
Indebtedness owed by Borrower, or (iii) result in or require the creation of any
Lien upon any assets or properties of Borrower except as expressly contemplated
in the Loan Documents.  Except as expressly contemplated in the Loan Documents,
no consent, approval, authorization or order of, and no notice to or filing with
any court or Governmental Authority or third party is required in connection
with the execution, delivery or performance by Borrower of this Second Amendment
or to consummate any transactions contemplated by this Second Amendment.

     C.   Enforceable Obligations.  This Second Amendment and the Credit
Agreement as amended by this Second Amendment will, on the due execution and
delivery hereof, constitute the legal, valid and binding obligations of
Borrower, enforceable in accordance with their terms except as such enforcement
may be limited by bankruptcy, insolvency or similar laws of general application
relating to the enforcement of creditors' rights and subject to general
principles of equity, regardless of whether considered in a proceeding in equity
or at law.

     D.   No Defaults.  No Default has occurred and is continuing.

     SECTION 6. Release of Certain Security Documents. Promptly following the
execution of this Second Amendment, Administrative Agent shall, at Borrower's
sole cost and expense, undertake to take such actions as reasonably necessary to
release the Security Documents identified in Sections 1, 2 and 3 of Schedule 2
to the Credit Agreement (prior to giving effect to this Second Amendment).

     SECTION 7. Reaffirmation of Credit Agreement. This Second Amendment shall
be deemed to be an amendment to the Credit Agreement, and the Credit Agreement,
as amended hereby, is hereby ratified, approved and confirmed in each and every
respect. All references to the Credit Agreement in any other document,
instrument, agreement or writing shall hereafter be deemed to refer to the
Credit Agreement as amended hereby.

                                       8
<PAGE>

     SECTION 8. Severability. If any term or provision of any Second Amendment
shall be determined to be illegal or unenforceable all other terms and
provisions of this Second Amendment shall nevertheless remain effective and
shall be enforced to the fullest extent permitted by applicable law.

     SECTION 9. Headings. The various headings of this Second Amendment are
inserted for convenience only and shall not affect the meaning or interpretation
of this Second Amendment or any provisions hereof or thereof.

     SECTION 10. Counterparts. This Second Amendment may be separately executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which when so executed shall be deemed to constitute one
and the same agreement.

     SECTION 11. GOVERNING LAW. THIS SECOND AMENDMENT SHALL BE DEEMED CONTRACTS
AND INSTRUMENTS MADE UNDER THE LAWS OF THE STATE OF TEXAS AND SHALL BE CONSTRUED
AND ENFORCED IN ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF TEXAS
AND THE LAWS OF THE UNITED STATES OF AMERICA.

     SECTION 12. Successors and Assigns. The provisions of this Second Amendment
shall be binding upon and inure to the benefit of the parties hereto and their
respective successor and assigns, except that Borrower may not assign or
otherwise transfer any of its rights under this Second Amendment without the
prior written consent of all Lenders.

     SECTION 13. ENTIRE AGREEMENT. THIS WRITTEN SECOND AMENDMENT AND THE OTHER
LOAN DOCUMENTS 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.

                            [SIGNATURE PAGES FOLLOW]

                                       9
<PAGE>

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


                             SPINNAKER EXPLORATION COMPANY, L.L.C.


                             By:   SPINNAKER EXPLORATION COMPANY,
                                   as Managing Member


                             By:  /s/ Robert M. Snell
                                -------------------------------------------
                             Name:  Robert M. Snell
                             Title: Vice President, CFO and Secretary


                             TORONTO DOMINION (TEXAS), INC.,
                             as Administrative Agent and as a Lender


                             By:  /s/ Jeffery R. Lents
                                -------------------------------------------
                             Name:  Jeffery R. Lents
                             Title: Vice President


                             CREDIT SUISSE FIRST BOSTON,
                             as Documentation Agent and as a Lender


                             By:  /s/ James P. Moran
                                -------------------------------------------
                             Name:  James P. Moran
                             Title: Director


                             By:  /s/ Brian T. Caldwell
                                -------------------------------------------
                             Name:  Brian T. Caldwell
                             Title: Vice President

                                      S-1
<PAGE>

                             THE TORONTO-DOMINION BANK,
                             as Issuer


                             By:  /s/ Jeffery R. Lents
                                -------------------------------------------
                             Name:  Jeffery R. Lents
                             Title: Manager, Syndications &
                                    Credit Administration


                                      S-2