<PAGE>
                                                                    EXHIBIT 10.2


--------------------------------------------------------------------------------



                       FIRST AMENDMENT TO CREDIT AGREEMENT

                                     BETWEEN

                           CONTANGO OIL & GAS COMPANY

                                       AND

                               GUARANTY BANK, FSB
                                    AS LENDER

                         Effective as of January 8, 2002

                       ----------------------------------

             REDUCING REVOLVING LINE OF CREDIT OF UP TO $50,000,000

                       -----------------------------------


--------------------------------------------------------------------------------


<PAGE>

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                          PAGE
                                                                          ----
<S>                                                                       <C>
ARTICLE I   DEFINITIONS ..................................................   1
1.01        Terms Defined Above ..........................................   1
1.02        Terms Defined in Agreement ...................................   1
1.03        References ...................................................   1
1.04        Articles and Sections ........................................   1
1.05        Number and Gender ............................................   1
ARTICLE II  AMENDMENTS ...................................................   2
2.01        Amendment of Section 1.2 .....................................   2
2.02        Amendment of Section 2.2 .....................................   3
2.03        Amendment of Section 2.6(a) ..................................   3
2.04        Amendment of Section 2.7 .....................................   3
2.05        Addition of Section 2.17 .....................................   4
2.06        Addition of Section 2.18 .....................................   4
2.07        Amendment to Preamble to Article III .........................   5
2.08        Amendment of Section 3.2 .....................................   5
2.09        Amendment of Section 3.3 .....................................   6
2.10        Amendment of Article IV ......................................   7
2.11        Amendment of Section 5.18 ....................................   7
2.12        Amendment of Section 5.20 ....................................   8
2.13        Amendment of Section 7.1 .....................................   8
2.14        Amendment of Section 8.7 .....................................   8
2.15        Amendment of Exhibit I .......................................   9
ARTICLE III CONDITIONS ...................................................   9
3.01        Receipt of Documents .........................................   9
3.02        Accuracy of Representations and Warranties ...................   9
3.03        Matters Satisfactory to Lender ...............................   9
ARTICLE IV  REPRESENTATIONS AND WARRANTIES ...............................   9
ARTICLE V   RATIFICATION .................................................  10
ARTICLE VI  MISCELLANEOUS ................................................  10
6.01        Scope of Amendment ...........................................  10
6.02        Agreement as Amended .........................................  10
6.03        Parties in Interest ..........................................  10
6.04        Rights of Third Parties ......................................  10
6.05        ENTIRE AGREEMENT .............................................  10
6.06        GOVERNING LAW ................................................  10
6.07        JURISDICTION AND VENUE .......................................  11
</TABLE>

                                        i








<PAGE>

                       FIRST AMENDMENT TO CREDIT AGREEMENT
                       -----------------------------------

     This FIRST AMENDMENT TO CREDIT AGREEMENT (this "First Amendment") is made
                                                     ---------------
and entered into effective as of January 8, 2002, between CONTANGO OIL & GAS
COMPANY, a Delaware corporation, (the "Borrower"), and GUARANTY BANK, FSB, a
                                       --------
federal savings bank (the "Lender").
                           ------

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

     WHEREAS, the above named parties did execute and exchange counterparts of
that certain Credit Agreement dated June 29, 2001 (the "Agreement"), to which
                                                        ---------
reference is here made for all purposes;

     WHEREAS, the parties subject to and bound by the Agreement are desirous of
amending the Agreement in the particulars hereinafter set forth;

     NOW, THEREFORE, in consideration of the mutual covenants and agreements of
the parties to the Agreement, as set forth therein, and the mutual covenants and
agreements of the parties hereto, as set forth in this First Amendment, the
parties hereto agree as follows:

                                    ARTICLE I
                                   DEFINITIONS

     1.01 Terms Defined Above. As used herein, each of the terms "Agreement,"
          -------------------                                     ---------
"Borrower," "First Amendment," and "Lender" shall have the meaning assigned to
 --------    ---------------        ------
such term hereinabove.

     1.02 Terms Defined in Agreement. As used herein, each term defined in the
          --------------------------
Agreement shall have the meaning assigned thereto in the Agreement, unless
expressly provided herein to the contrary.

     1.03 References. References in this First Amendment to Article or Section
          ----------
numbers shall be to Articles and Sections of this First Amendment, unless
expressly stated herein to the contrary. References in this First Amendment to
"hereby," "herein," hereinafter," hereinabove," "hereinbelow," "hereof," and
"hereunder" shall be to this First Amendment in its entirety and not only to the
particular Article or Section in which such reference appears.

     1.04 Articles and Sections. This First Amendment, for convenience only, has
          ---------------------
been divided into Articles and Sections and it is understood that the rights,
powers, privileges, duties, and other legal relations of the parties hereto
shall be determined from this First Amendment as an entirety and without regard
to such division into Articles and Sections and without regard to headings
prefixed to such Articles and Sections.

     1.05 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

                                        1

<PAGE>

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 and plural shall be equally applicable to the
plural or singular, as the case may be.

                                   ARTICLE II
                                   AMENDMENTS
                                   ----------

     The Borrower and the Lender hereby amend the Agreement in the following
particulars:

     2.01 Amendment of Section 1.2. Section 1.2 of the Agreement shall be
          ------------------------
amended to read as follows:

     Section 1.2 of the Agreement is hereby amended to add and/or amend the
     following definitions to read as follows, in proper alphabetical order:

     "Available Commitment" shall mean, at any time, an amount equal to the
      --------------------
     remainder, if any, of (a) the Borrowing Base in effect at such time minus
     (b) the sum of the Loan Balance at such time.

     "Commitment" shall mean the obligation of the Lender, subject to applicable
      ----------
     provisions of this Agreement, to make Loans to or for the benefit of the
     Borrower pursuant to Section 2.1 and to issue Letters of Credit pursuant to
     Section 2.17.

     "L/C Exposure" shall mean, at any time, the aggregate maximum amount
      ------------
     available to be drawn under outstanding Letters of Credit at such time.

     "Letter of Credit" shall mean any standby letter of credit issued by the
      ----------------
     Lender for the account of the Borrower pursuant to Section 2.17.

     "Letter of Credit Application" shall mean the standard letter of credit
      ----------------------------
     application employed by the Lender from time to time in connection with
     letters of credit.

     "Letter of Credit Fee" shall mean each fee payable to the Lender by the
      --------------------
     Borrower pursuant to Section 2.18 upon or in connection with the issuance
     of a Letter of Credit.

     "Loan" shall mean any loan made by the Lender to or for the benefit of the
      ----
     Borrower pursuant to this Agreement and any payment made by the Lender
     under a Letter of Credit.

     "Loan Balance" shall mean, at any time, the outstanding principal balance
      ------------
     of the Note plus the L/C Exposure at such time.

     "Loan Documents" shall mean this Agreement, the Note, the Letter of Credit
      --------------
     Applications, the Letters of Credit, the Security Instruments, and all
     other documents and instruments now or hereafter delivered pursuant to the
     terms of or in connection with this Agreement, the Note, the Letter of
     Credit Applications, the Letters of Credit, or the Security Instruments,
     and all renewals and extensions of, amendments

                                        2

<PAGE>

     and supplements to, and restatements of, any or all of the foregoing from
     time to time in effect.

     "Obligations" shall mean, without duplication, (a) all Indebtedness
      -----------
     evidenced by the Note, (b) the Reimbursement Obligations, (c) the undrawn,
     unexpired amount of all outstanding Letters of Credit, (d) the obligation
     of the Borrower for the payment of Commitment Fees, Facility Fees, Letter
     of Credit Fees, and Engineering Fees, (e) all obligations and liabilities
     whether now existing or hereafter arising of the Borrower to the Lender in
     connection with any Commodity Hedge Agreement or Rate Management
     Transaction, and (f) all other obligations and liabilities of the Borrower
     to the Lender, now existing or hereafter incurred, under, arising out of or
     in connection with any Loan Document, and to the extent that any of the
     foregoing includes or refers to the payment of amounts deemed or
     constituting interest, only so much thereof as shall have accrued, been
     earned and which remains unpaid at each relevant time of determination.

     "Reimbursement Obligation" shall mean the obligation of the Borrower to
      ------------------------
     provide to the Lender or reimburse the Lender for any amounts payable,
     paid, or incurred by the Lender with respect to Letters of Credit.

     2.02 Amendment of Section 2.2. Section 2.2 of the Agreement is hereby
          ------------------------
amended to read as follows:

     "2.2 Use of Loan Proceeds and Letters of Credit. (a) Proceeds of all Loans
          ------------------------------------------
     shall be used solely to refinance existing bank debt and for funding
     development, exploration and acquisition activities and other general
     corporate purposes.

     (b) Letters of Credit shall be used solely for general corporate purposes;
     provided, however, no Letter of Credit may be used in lieu or in support of
     stay or appeal bonds."

     2.03 Amendment of Section 2.6(a). Section 2.6(a) is amended to read as
          ---------------------------
follows:

     "2.6 Borrowing Base Determination. (a) The Borrowing Base as of January 1,
          ----------------------------
     2002, is acknowledged by the Borrower and the Lender to be $17,000.000.00.
     Commencing on February 1, 2002, and continuing thereafter on the first day
     of each calendar month through the next Borrowing Base review the amount of
     the Borrowing Base shall be reduced by $450,000.00."

     2.04 Amendment of Section 2.7. Section 2.7 of the Agreement is hereby
          ------------------------
amended to read as follows:

     "2.7 Mandatory Prepayments. If at any time the sum of the Loan Balance and
          ---------------------
     the L/C Exposure exceeds the Borrowing Base then in effect, the Borrower
     shall, within 30 days of notice from the Lender of such occurrence, (a)
     prepay, or make arrangements acceptable to the Lender for the prepayment
     of, the amount of such excess for application on the Loan Balance, (b)
     provide additional collateral, of character and value satisfactory to the
     Lender in its sole discretion, to secure the

                                        3

<PAGE>

     Obligations by the execution and delivery to the Lender of security
     instruments in form and substance satisfactory to the Lender, or (c) effect
     any combination of the alternatives described in clauses (a) and (b) of
     this Section and acceptable to the Lender in its sole discretion. In the
     event that a mandatory prepayment is required under this Section and the
     Loan Balance is less than the amount required to be prepaid, the Borrower
     shall repay the entire Loan Balance and, in accordance with the provisions
     of the relevant Letter of Credit Applications executed by the Borrower or
     otherwise to the satisfaction of the Lender, deposit with the Lender, as
     additional collateral securing the Obligations, an amount of cash, in
     immediately available funds, equal to the L/C Exposure minus the Borrowing
     Base. The cash deposited with the Lender in satisfaction of the requirement
     provided in this Section may be invested, at the sole discretion of the
     Lender and then only at the express direction of the Borrower as to
     investment vehicle and maturity (which shall be no later than the latest
     expiry date of any then outstanding Letter of Credit), for the account of
     the Borrower in cash or cash equivalent investments offered by or through
     the Lender."

     2.05 Addition of Section 2.17. A new section designated "Section 2.17" is
          ------------------------
hereby added to the Agreement to read as follows:

     "2.17 Letter of Credit Facility. (a) Upon the terms and conditions
           -------------------------
     (including, without limitation, the right of the Lender to decline to issue
     any Letter of Credit so long as any Default or Event of Default exists) and
     relying on the representations and warranties contained in this Agreement,
     the Lender agrees, during the Commitment Period, to issue Letters of Credit
     following the receipt not less than two Business Days prior to the
     requested date for issuance of the relevant Letter of Credit, of a Letter
     of Credit Application executed by the Borrower; provided, however, (a) no
     Letter of Credit shall have an expiration date which is more than 60 days
     after the issuance thereof or subsequent to the Commitment Termination
     Date, and (b) the Lender shall not be obligated to issue any Letter of
     Credit if (i) the face amount thereof would exceed the Available
     Commitment, or (ii) after giving effect to the issuance thereof, (A) the
     L/C Exposure, when added to the Loan Balance then outstanding, would exceed
     the Borrowing Base then in effect, or (B) the L/C Exposure would exceed
     $3,000,000.

     (b) Should the Lender be called upon by the beneficiary of any Letter of
     Credit to honor all or any portion of the commitment thereunder, whether
     upon the presentation of drafts or otherwise, such payment by the Lender on
     account of such Letter of Credit shall be treated, for all purposes, as a
     Floating Rate Loan and an advance against the Note."

     2.06 Addition of Section 2.18. A new section designated "Section 2.18" is
          ------------------------
hereby added to the Agreement to read as follows:

     "2.18 Letter of Credit Fee. In addition to interest on the Note as provided
           --------------------
     herein and all other fees payable hereunder, the Borrower agrees to pay to
     the Lender, on the date of issuance of each Letter of Credit, a fee equal
     to two percent (2%) per annum, or a minimum of $500, calculated on the
     basis of a year of 365 or 366 days, as the

                                        4

<PAGE>

     case may be, and actual days elapsed (including the first day but excluding
     the last day), on the face amount of such Letter of Credit during the
     period for which such Letter of Credit is issued; provided, however, in the
     event such Letter of Credit is canceled prior to its original expiry date
     or a payment is made by the Lender with respect to such Letter of Credit,
     the Lender shall, within 30 days after such cancellation or the making of
     such payment, rebate to the Borrower the unearned portion of such fee. The
     Borrower also agrees to pay to the Lender on demand its customary letter of
     credit transactional fees, including, without limitation, amendment fees,
     payable with respect to each Letter of Credit."

     2.07 Amendment to Preamble to Article III. The preamble to Article III is
          ------------------------------------
hereby amended to read as follows:

     "The obligations of the Lender to enter into this Agreement and to make
     Loans and issue Letters of Credit are subject to the satisfaction of the
     following conditions precedent:"

     2.08 Amendment of Section 3.2. Section 3.2 of the Agreement is hereby
          ------------------------
amended to read as follows:

     "3.2 Each Loan and Letter of Credit. In addition to the conditions
          ------------------------------
     precedent stated elsewhere herein, the Lender shall not be obligated to
     make any Loan or issue any Letter of Credit unless:

     (a) the Borrower shall have delivered to the Lender a Borrowing Request at
     least the requisite time prior to the requested date for the relevant Loan,
     or a Letter of Credit Application at least two Business Days prior to the
     requested issuance date for the relevant Letter of Credit and each
     statement or certification made in such Borrowing Request or Letter of
     Credit Application, as the case may be, shall be true and correct in all
     material respects on the requested date for such Loan or the issuance of
     such Letter of Credit;

     (b) no Event of Default or Default shall exist or will occur as a result of
     the making of the requested Loan or the issuance of the requested Letter of
     Credit;

     (c) if requested by the Lender, the Borrower shall have delivered evidence
     satisfactory to the Lender substantiating any of the matters contained in
     this Agreement which are necessary to enable the Borrower to qualify for
     such Loan or the issuance of such Letter of Credit;

     (d) the Lender shall have received, reviewed, and approved such additional
     documents and items as described in Section 3.1 as may be requested by the
     Lender with respect to such Loan or Letter of Credit;

     (e) no event shall have occurred which, in the reasonable opinion of the
     Lender, could have a Material Adverse Effect;

                                        5

<PAGE>

     (f) each of the representations and warranties contained in this Agreement
     shall be true and correct and shall be deemed to be repeated by the
     Borrower as if made on the requested date for such Loan or the issuance of
     such Letter of Credit;

     (g) all of the Security Instruments shall be in full force and effect and
     provide to the Lender the security intended thereby;

     (h) neither the consummation of the transactions contemplated hereby nor
     the making of such Loan the issuance of such Letter of Credit shall
     contravene, violate, or conflict with any Requirement of Law;

     (i) the Borrower shall hold full legal title to the Collateral pledged by
     such entity and be the sole beneficial owner thereof;

     (j) the Lender shall have received the payment of all Engineering Fees,
     Facility Fees, Letter of Credit Fees, and other fees payable to the Lender
     hereunder and reimbursement from the Borrower, or special legal counsel for
     the Lender shall have received payment from the Borrower, for (i) all
     reasonable fees and expenses of counsel to the Lender for which the
     Borrower is responsible pursuant to applicable provisions of this Agreement
     and for which invoices have been presented as of or prior to the date of
     the relevant Loan or Letter of Credit Application, and (ii) estimated fees
     charged by filing officers and other public officials incurred or to be
     incurred in connection with the filing and recordation of any Security
     Instruments, for which invoices have been presented as of or prior to the
     date of the requested Loan or Letter of Credit Application; and

     (k) all matters incident to the consummation of the transactions hereby
     contemplated shall be satisfactory to the Lender."

     2.09 Amendment of Section 3.3. Section 3.3 of the Agreement is hereby
          ------------------------
amended to read as follows:

     "3.3 Mortgage of Oil and Gas Properties. The following documents will be
          ----------------------------------
     required upon the execution of this First Amendment:

     (a) Deed of Trust, Security Agreement, Assignment of Production, and
     Financing Statement from the Borrower covering all Oil and Gas Properties
     of the Borrower and all improvements, personal property, and fixtures
     related thereto;

     (b) Financing Statements from the Borrower, as debtors, constituent to the
     instrument described in clause (a) above;

     (c) undated letters, in form and substance satisfactory to the Lender, from
     the Borrower to each purchaser of production and disburser of the proceeds
     of production from or attributable to the Mortgaged Properties, together
     with additional letters with the addressees left blank, authorizing and
     directing the addressees to make future payments attributable to production
     from the Mortgaged Properties directly to the Lender;"

                                       6

<PAGE>

     2.10 Amendment of Article IV. The preamble to Article IV of the Agreement
          -----------------------
is hereby amended to read as follows:

     "To induce the Lender to enter into this Agreement and to make the Loans
     and issue Letters of Credit, the Borrower represents and warrants to the
     Lender (which representations and warranties shall survive the delivery of
     the Note) that:"

     2.11 Amendment of Section 5.18. Section 5.18 of the Agreement is hereby
          -------------------------
amended to read as follows:

     "5.18 INDEMNIFICATION. INDEMNIFY AND HOLD THE LENDER AND ITS SHAREHOLDERS,
           ---------------
     OFFICERS, DIRECTORS, EMPLOYEES, AGENTS, ATTORNEYS-IN-FACT, AND AFFILIATES
     AND EACH TRUSTEE FOR THE BENEFIT OF THE LENDER UNDER ANY SECURITY
     INSTRUMENT HARMLESS FROM AND AGAINST ANY AND ALL CLAIMS, LOSSES, DAMAGES,
     LIABILITIES, FINES, PENALTIES, CHARGES, ADMINISTRATIVE AND JUDICIAL
     PROCEEDINGS AND ORDERS, JUDGMENTS, REMEDIAL ACTIONS, REQUIREMENTS AND
     ENFORCEMENT ACTIONS OF ANY KIND, AND ALL COSTS AND EXPENSES INCURRED IN
     CONNECTION THEREWITH (INCLUDING, WITHOUT LIMITATION, ATTORNEYS' FEES AND
     EXPENSES), ARISING DIRECTLY OR INDIRECTLY, IN WHOLE OR IN PART, FROM (A)
     THE PRESENCE OF ANY HAZARDOUS SUBSTANCES ON, UNDER, OR FROM ANY PROPERTY OF
     THE BORROWER, WHETHER PRIOR TO OR DURING THE TERM HEREOF, (B) ANY ACTIVITY
     CARRIED ON OR UNDERTAKEN ON OR OFF ANY PROPERTY OF THE BORROWER, WHETHER
     PRIOR TO OR DURING THE TERM HEREOF, AND WHETHER BY THE BORROWER OR ANY
     PREDECESSOR IN TITLE, EMPLOYEE, AGENT, CONTRACTOR, OR SUBCONTRACTOR OF THE
     BORROWER OR ANY OTHER PERSON AT ANY TIME OCCUPYING OR PRESENT ON SUCH
     PROPERTY, IN CONNECTION WITH THE HANDLING, TREATMENT, REMOVAL, STORAGE,
     DECONTAMINATION, CLEANUP, TRANSPORTATION, OR DISPOSAL OF ANY HAZARDOUS
     SUBSTANCES AT ANY TIME LOCATED OR PRESENT ON OR UNDER SUCH PROPERTY, (C)
     ANY RESIDUAL CONTAMINATION ON OR UNDER ANY PROPERTY OF THE BORROWER, (D)
     ANY CONTAMINATION OF ANY PROPERTY OR NATURAL RESOURCES ARISING IN
     CONNECTION WITH THE GENERATION, USE, HANDLING, STORAGE, TRANSPORTATION OR
     DISPOSAL OF ANY HAZARDOUS SUBSTANCES BY THE BORROWER OR ANY EMPLOYEE,
     AGENT, CONTRACTOR, OR SUBCONTRACTOR OF THE BORROWER WHILE SUCH PERSONS ARE
     ACTING WITHIN THE SCOPE OF THEIR RELATIONSHIP WITH THE BORROWER,
     IRRESPECTIVE OF WHETHER ANY OF SUCH ACTIVITIES WERE OR WILL BE UNDERTAKEN
     IN ACCORDANCE WITH APPLICABLE REQUIREMENTS OF LAW, OR (E) THE PERFORMANCE
     AND ENFORCEMENT OF ANY LOAN DOCUMENT, ANY ALLEGATION BY ANY BENEFICIARY OF
     A LETTER OF CREDIT OF A WRONGFUL DISHONOR BY THE LENDER OF A CLAIM OR DRAFT
     PRESENTED THEREUNDER, OR

                                        7

<PAGE>

     ANY OTHER ACT OR OMISSION IN CONNECTION WITH OR RELATED TO ANY LOAN
     DOCUMENT OR THE TRANSACTIONS CONTEMPLATED THEREBY, INCLUDING, WITHOUT
     LIMITATION, ANY OF THE FOREGOING IN THIS SECTION ARISING FROM NEGLIGENCE,
     WHETHER SOLE OR CONCURRENT, ON THE PART OF THE LENDER OR ANY OF ITS
     SHAREHOLDERS, OFFICERS, DIRECTORS, EMPLOYEES, AGENTS, ATTORNEYS-IN-FACT, OR
     AFFILIATES OR ANY TRUSTEE FOR THE BENEFIT OF THE LENDER UNDER ANY SECURITY
     INSTRUMENT; WITH THE FOREGOING INDEMNITY SURVIVING SATISFACTION OF ALL
     OBLIGATIONS AND THE TERMINATION OF THIS AGREEMENT, UNLESS ALL SUCH
     OBLIGATIONS HAVE BEEN SATISFIED WHOLLY IN CASH FROM THE BORROWER AND NOT BY
     WAY OF REALIZATION AGAINST ANY COLLATERAL OR THE CONVEYANCE OF ANY PROPERTY
     IN LIEU THEREOF, PROVIDED THAT SUCH INDEMNITY SHALL NOT EXTEND TO ANY ACT
     OR OMISSION BY THE LENDER WITH RESPECT TO ANY PROPERTY SUBSEQUENT TO THE
     LENDER BECOMING THE OWNER OF SUCH PROPERTY AND WITH RESPECT TO WHICH
     PROPERTY SUCH CLAIM, LOSS, DAMAGE, LIABILITY, FINE, PENALTY, CHARGE,
     PROCEEDING, ORDER, JUDGMENT, ACTION, OR REQUIREMENT ARISES SUBSEQUENT TO
     THE ACQUISITION OF TITLE THERETO BY THE LENDER."

     2.12  Amendment of Section 5.20. Section 5.20 of the Agreement is amended
           -------------------------
to read as follows:

     "5.20 Pledge of Collateral. Borrower agrees to pledge certain of the Oil
           --------------------
     and Gas Properties described in the Purchase and Sale Agreement dated
     effective as of January 1, 2002, between the Borrower and Juneau
     Exploration L.P. and conveyed to Borrower on April 1, 2002, and July 1,
     2002. The Lender will determine at its sole descretion which of the Oil and
     Gas Properties to be pledged.

     2.13  Amendment of Section 7.1. Subparagraph (e) of Section 7.1 of the
           ------------------------
Agreement is hereby amended to read as follows:

     "(e) the Borrower shall be unable to satisfy any condition or cure any
     circumstance specified in Article III, the satisfaction or curing of which
     is precedent to the right of the Borrower to obtain a Loan or the issuance
     of a Letter of Credit, and such inability shall continue for a period in
     excess of 30 days;"

     2.14  Amendment of Section 8.7. Section 8.7 of the Agreement is hereby
           ------------------------
amended to read as follows:

     "8.7  No Waiver; Rights Cumulative. No course of dealing on the part of the
           ----------------------------
     Lender, its officers or employees, nor any failure or delay by the Lender
     with respect to exercising any of its rights under any Loan Document shall
     operate as a waiver thereof. The rights of the Lender under the Loan
     Documents shall be cumulative and the exercise or partial exercise of any
     such right shall not preclude the exercise of

                                        8

<PAGE>

     any other right. Neither the making of any Loan nor the issuance of a
     Letter of Credit shall constitute a waiver of any of the covenants,
     warranties, or conditions of the Borrower contained herein. In the event
     the Borrower is unable to satisfy any such covenant, warranty, or
     condition, neither the making of any Loan nor the issuance of a Letter of
     Credit shall have the effect of precluding the Lender from thereafter
     declaring such inability to be an Event of Default as hereinabove
     provided."

     2.15 Amendment of Exhibit I. Exhibit I, i.e. the "Form of Promissory Note"
          ----------------------
shall be as set forth on Exhibit I to this First Amendment.

                                  ARTICLE III
                                   CONDITIONS
                                   ----------

     The obligation of the Lender to amend the Agreement as provided herein is
subject to the fulfillment of the following conditions precedent:

     3.01 Receipt of Documents. The Lender shall have received, reviewed, and
          --------------------
approved the following documents and other items, appropriately executed when
necessary and in form and substance satisfactory to the Lender:

     (a)  multiple counterparts of this First Amendment, as requested by the
          Lender;

     (b)  the Note;

     (c)  multiple counterparts of the documents listed in Section 3.3 above;

     (d)  closing of purchase of certain Oil and Gas Properties from Juneau
          Exploration L.P.;

     (e)  payment of Facility Fee in the amount of $52,500.00; and

     (f)  such other agreements, documents, items, instruments, opinions,
          certificates, waivers, consents, and evidence as the Lender may
          reasonably request.

     3.02 Accuracy of Representations and Warranties. The representations and
          ------------------------------------------
warranties contained in Article IV of the Agreement and this First Amendment
shall be true and correct.

     3.03 Matters Satisfactory to Lender. All matters incident to the
          ------------------------------
consummation of the transactions contemplated hereby shall be satisfactory to
the Lender.

                                   ARTICLE IV
                         REPRESENTATIONS AND WARRANTIES
                         ------------------------------

     The Borrower hereby expressly re-makes, in favor of the Lender, all of the
representations and warranties set forth in Article IV of the Agreement, and
represents and warrants that all such representations and warranties remain true
and unbreached.

                                        9

<PAGE>

                                   ARTICLE V
                                  RATIFICATION
                                  ------------

     Each of the parties hereto does hereby adopt, ratify, and confirm the
Agreement and the other Loan Documents, in all things in accordance with the
terms and provisions thereof, as amended by this First Amendment.

                                   ARTICLE VI
                                  MISCELLANEOUS
                                  -------------

     6.01 Scope of Amendment. The scope of this First Amendment is expressly
          ------------------
limited to the matters addressed herein and this First Amendment shall not
operate as a waiver of any past, present, or future breach, Default, or Event of
Default under the Agreement. except to the extent, if any, that any such breach,
Default, or Event of Default is remedied by the effect of this First Amendment.

     6.02 Agreement as Amended. All references to the Agreement in any document
          --------------------
heretofore or hereafter executed in connection with the transactions
contemplated in the Agreement shall be deemed to refer to the Agreement as
amended by this First Amendment.

     6.03 Parties in Interest. All provisions of this First Amendment shall be
          -------------------
binding upon and shall inure to the benefit of the Borrower, the Lender and
their respective successors and assigns.

     6.04 Rights of Third Parties. All provisions herein are imposed solely and
          -----------------------
exclusively for the benefit of the Lender and the Borrower, and no other Person
shall have standing to require satisfaction of such provisions in accordance
with their terms and any or all of such provisions may be freely waived in whole
or in part by the Lender at any time if in its sole discretion it deems it
advisable to do so.

     6.05 ENTIRE AGREEMENT. THIS FIRST AMENDMENT CONSTITUTES THE ENTIRE
          ----------------
AGREEMENT BETWEEN THE PARTIES HERETO WITH RESPECT TO THE SUBJECT HEREOF AND
SUPERSEDES ANY PRIOR AGREEMENT, WHETHER WRITTEN OR ORAL, BETWEEN SUCH PARTIES
REGARDING THE SUBJECT HEREOF. FURTHERMORE IN THIS REGARD, THIS FIRST AMENDMENT,
THE AGREEMENT, THE NOTE, THE SECURITY INSTRUMENTS, AND THE OTHER WRITTEN
DOCUMENTS REFERRED TO IN THE AGREEMENT OR EXECUTED IN CONNECTION WITH OR AS
SECURITY FOR THE NOTE REPRESENT, COLLECTIVELY, THE FINAL AGREEMENT AMONG THE
PARTIES THERETO AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO
UNWRITTEN ORAL AGREEMENTS AMONG THE PARTIES.

     6.06 GOVERNING LAW. THIS FIRST AMENDMENT, THE AGREEMENT AND THE NOTE SHALL
          -------------
BE DEEMED TO BE CONTRACTS MADE UNDER AND SHALL BE CONSTRUED IN ACCORDANCE WITH
AND GOVERNED BY THE LAWS OF THE STATE OF TEXAS. THE PARTIES ACKNOWLEDGE AND
AGREE THAT THIS AGREEMENT AND THE NOTE AND THE TRANSACTIONS CONTEMPLATED HEREBY
BEAR A NORMAL, REASONABLE, AND SUBSTANTIAL RELATIONSHIP TO THE STATE OF TEXAS.


                                       10

<PAGE>

     6.07 JURISDICTION AND VENUE. ALL ACTIONS OR PROCEEDINGS WITH RESPECT TO,
          ----------------------
ARISING DIRECTLY OR INDIRECTLY IN CONNECTION WITH, OUT OF, RELATED TO, OR FROM
THIS FIRST AMENDMENT, THE AGREEMENT OR ANY OTHER LOAN DOCUMENT MAY BE LITIGATED
IN COURTS HAVING SITUS IN HARRIS COUNTY, TEXAS. EACH OF THE BORROWER AND THE
LENDER HEREBY SUBMITS TO THE JURISDICTION OF ANY LOCAL, STATE, OR FEDERAL COURT
LOCATED IN HARRIS COUNTY, TEXAS, AND HEREBY WAIVES ANY RIGHTS IT MAY HAVE TO
TRANSFER OR CHANGE THE JURISDICTION OR VENUE OF ANY LITIGATION BROUGHT AGAINST
IT BY THE BORROWER OR THE LENDER IN ACCORDANCE WITH THIS SECTION.

     IN WITNESS WHEREOF, this First Amendment to Credit Agreement is executed
effective the date first hereinabove written.

                                      BORROWER
                                      --------

                                      CONTANGO OIL & GAS COMPANY


                                      By:   /s/ WILLIAM H. GIBBONS
                                         -----------------------------
                                            William H. Gibbons
                                            Vice President and Treasurer

                                       11

<PAGE>

                                      LENDER
                                      ------

                                      GUARANTY BANK, FSB

                                      By: /s/ RICHARD E. MENCHACA
                                         ---------------------------
                                          Richard E. Menchaca
                                          Vice President

                                       12

<PAGE>

                                    EXHIBIT I
                                    ---------

                             FORM OF PROMISSORY NOTE

$50,000,000.00                    Houston, Texas                January 8, 2002

     FOR VALUE RECEIVED and WITHOUT GRACE, the undersigned ("Maker") promises to
pay to the order of GUARANTY BANK, FSB ("Payee"), at its banking quarters in
Houston, Harris County, Texas, the sum of FIFTY MILLION DOLLARS
($50,000,000.00), or so much thereof as may be advanced against this Note
pursuant to the Credit Agreement dated June 29, 2001, as amended by First
Amendment of even date herewith by and between Maker and Payee (as further
amended, restated, or supplemented from time to time, the "Credit Agreement"),
together with interest at the rates and calculated as provided in the Credit
Agreement.

     Reference is hereby made to the Credit Agreement for matters governed
thereby, including, without limitation, certain events which will entitle the
holder hereof to accelerate the maturity of all amounts due hereunder.
Capitalized terms used but not defined in this Note shall have the meanings
assigned to such terms in the Credit Agreement.

     This Note is issued pursuant to, is the "Note" under, and is payable as
provided in the Credit Agreement. Subject to compliance with applicable
provisions of the Credit Agreement, Maker may at any time pay the full amount or
any part of this Note without the payment of any premium or fee, but such
payment shall not, until this Note is fully paid and satisfied, excuse the
payment as it becomes due of any payment on this Note provided for in the Credit
Agreement.

     THIS NOTE SHALL BE GOVERNED AND CONTROLLED BY THE LAWS OF THE STATE OF
TEXAS WITHOUT GIVING EFFECT TO PRINCIPLES THEREOF RELATING TO CONFLICTS OF LAW;
PROVIDED, HOWEVER, THAT CHAPTER 345 OF THE TEXAS FINANCE CODE (WHICH REGULATES
CERTAIN REVOLVING CREDIT LOAN ACCOUNTS AND REVOLVING TRIPARTY ACCOUNTS) SHALL
NOT APPLY TO THIS NOTE.

                                         MAKER:

                                         CONTANGO OIL & GAS COMPANY

                                         By:_________________________________
                                                 William H. Gibbons
                                                 Vice President and Treasurer