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                                                                    EXHIBIT 10.4

                                     WARRANT
                           TO PURCHASE COMMON STOCK OF
                           CONTANGO OIL & GAS COMPANY
                              A NEVADA CORPORATION

                           EXPIRING DECEMBER 29, 2004

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
         UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR REGISTERED OR
         QUALIFIED UNDER ANY STATE SECURITIES LAWS. THE SECURITIES REPRESENTED
         BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE
         SOLD, TRANSFERRED, PLEDGED OR HYPOTHECATED (EXCEPT AS PERMITTED
         PURSUANT TO THAT CERTAIN SECURITIES PURCHASE AGREEMENT DATED AS OF
         DECEMBER 29,1999 AMONG CONTANGO OIL & GAS COMPANY (THE "COMPANY") AND
         THE HOLDER (THE "SECURITIES PURCHASE AGREEMENT"), TO THE EFFECT THAT
         THE PROPOSED TRANSACTION DOES NOT REQUIRE REGISTRATION OR QUALIFICATION
         UNDER FEDERAL OR STATE SECURITIES LAWS.

                            THIS IS TO CERTIFY THAT:

         Trust Company of the West, a California trust company, in its
capacities as Investment Manager pursuant to the Investment Management Agreement
dated as of June 6, 1988 between General Mills, Inc. and the Trust Company of
the West and as Custodian pursuant to the Custody Agreement dated as of February
6, 1989 among General Mills, Inc., the Trust Company of the West and State
Street Bank and Trust Company, as Trustee ("HOLDER"), or registered assigns, is
entitled to purchase from the Company at any time on and after the date hereof
but not later than 5 p.m., Central Standard Time, on December 29, 2004 (the
"EXPIRATION DATE"), Three Hundred Seventy Thousand Three Hundred Seventy
(370,370) Stock Units, in whole or in part, at a per Stock Unit purchase price
at any date equal to the Purchase Price (as defined below), all on the terms and
conditions hereinbelow provided.

         Section 1. Certain Definitions. Initially capitalized terms not
otherwise defined herein shall have the meanings ascribed to such terms in the
Securities Purchase Agreement. As used in this Warrant:

                  "5-DAY AVERAGE PRICE" per share of Common Stock, for purposes
of any provision herein at the date specified in such provision, shall mean the
average closing price of the Common Stock on the [securities exchange or other
national market system on which the Common Stock is then listed] over the
5-trading day period immediately prior to such date. NOTE: STOCK NOW TRADES ON
OTC-BB

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                  "30-DAY AVERAGE PRICE" per share of Common Stock, for purposes
of any provision herein at the date specified in such provision, shall mean the
average closing price of the Common Stock on the [securities exchange or other
national market system on which the Common Stock is then listed] over the
30-trading day period immediately prior to such date.

                  "ADDITIONAL SHARES OF COMMON STOCK" shall mean all shares of
Common Stock issued by the Company after the Closing Date other than (i) any
shares of Common Stock issued pursuant to the outstanding warrants listed on
Attachment 1, (ii) any shares of Common Stock issued pursuant to options, rights
or warrants to purchase Common Stock issued pursuant to the Company's 1999 Stock
Incentive Plan, (iii) any shares of Common Stock issued to the Holder pursuant
to the preemptive rights in its favor set forth in Section 6 of the Securities
Purchase Agreement, and (iv) any shares of Common Stock issued pursuant to the
Company's agreement with Juneau Exploration dated as of September 1, 1999.

                  "AGGREGATE PURCHASE PRICE" shall have the meaning given in
Section 2 below.

                  "APPRAISED VALUE" shall mean the fair market value of all
outstanding Common Stock, as determined by a written appraisal (the "APPRAISAL")
prepared by a national or major regional investment bank acceptable to the Board
of Directors of the Company and the Holder. "Fair market value" is defined for
this purpose as the price in a single transaction determined on a going-concern
basis that would be agreed upon by the most likely hypothetical buyer for 100%
of the equity capital of the Company. In the event that the Company and Holder
cannot, in good faith, agree upon an investment bank, then the Company, on the
one hand, and Holder, on the other hand, shall each select an investment bank,
the two investment banks so selected shall select a third investment bank who
shall be directed to prepare the Appraisal and the term Appraised Value shall
mean the appraised value set forth in the Appraisal prepared in accordance with
this definition. [The Company shall pay for the cost of any such Appraisal.]

                  "BOARD OF DIRECTORS" shall mean the duly appointed board of
directors of the Company.

                  "BUSINESS DAY" shall mean a day, other than a Saturday, Sunday
or legal holiday on which commercial banks are authorized or obligated by law or
executive order to close in the State of Texas.

                  "COMMISSION" shall mean the Securities and Exchange
Commission.

                  "COMMON STOCK" shall mean the Company's authorized common
stock, $.04 par value per share, irrespective of class unless otherwise
specified, as constituted on the date of original issuance of this Warrant, and
any stock into which such common stock may thereafter be changed, and shall also
include stock of the Company of any other class, which is not preferred as to
dividends or assets over any other class of stock of the Company and which is
not subject to redemption, issued to the holders of shares of Common Stock upon
any reclassification thereof.

                  "CONVERTIBLE SECURITIES" shall mean evidences of indebtedness,
shares of stock or other securities which are convertible into or exchangeable
for Additional Shares of Common

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Stock, either immediately or upon the arrival of a specified date or the
happening of a specified event.

                  "CURRENT MARKET PRICE" per share of Common Stock for the
purposes of any provision of this Warrant at a date herein specified, shall mean
[the greater of (i) the 30-Day Average Price of the Common Stock or (ii) the
5-Day Average Price of the Common Stock; provided, that if the Current Market
Price per share of Common Stock cannot be ascertained by such methods, then the
Current Market Price per share of Common Stock shall be deemed to be the greater
of (i) the net book value per share of Common Stock, determined in accordance
with generally accepted accounting principles, or (ii) the fair value per share
of Common Stock determined pursuant to the Appraised Value.]

                  "CURRENT WARRANT PRICE" per share of Common Stock, for the
purpose of any provision of this Warrant at the date herein specified, shall
mean the amount equal to the quotient resulting from dividing the Purchase Price
per Stock Unit in effect on such date by the number of shares (including any
fractional share) of Common Stock comprising a Stock Unit on such date.

                  "PERSON" shall mean any individual, corporation, partnership,
association, joint stock company, trust or trustee thereof, estate or executor
thereof, unincorporated organization or joint venture, court or governmental
unit or any agency or subdivision thereof, or any other legally recognizable
entity.

                  "PURCHASE PRICE" shall mean $1.00 per Stock Unit.

                  "SECURITIES ACT" shall mean the Securities Act of 1933, as
amended, or any similar federal statute, and the rules and regulations of the
Commission thereunder, all as the same shall be in effect at the time.

                  "STOCK UNIT" shall mean one share of Common Stock, as such
Common Stock was constituted on the date of original issue of this Warrant and
thereafter shall mean such number of shares (including any fractional shares) of
Common Stock as shall result from the adjustments specified in Section 4 of this
Warrant.

                  "WARRANT" shall mean this Warrant, evidencing rights to
purchase shares of Common Stock, and all Warrants issued upon transfer, division
or combination of, or in substitution for, this Warrant. All Warrants shall at
all times be identical as to terms and conditions and date, except as to the
Common Stock for which they may be exercised.

                  "WARRANT STOCK" shall mean the shares of Common Stock
purchasable by the Holder upon the exercise hereof.

         Section 2. Exercise of Warrant. The holder of this Warrant may, at any
time on or after the date hereof but not later than the Expiration Date,
exercise this Warrant in whole or in part for the number of Stock Units which
such holder is then entitled to purchase hereunder. In order to exercise this
Warrant, in whole or in part, the holder hereof shall deliver to the Company at
its office maintained for such purpose pursuant to Section 16: (i) a written
notice of such holder's election to exercise this Warrant, (ii) this Warrant,
and (iii) the total purchase price for the shares

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being purchased upon such exercise by (a) delivery in cash, by wire transfer or
certified or official bank check of immediately available funds in an amount
equal to the product of the Purchase Price multiplied by the number of Stock
Units being purchased upon such exercise (the "AGGREGATE PURCHASE PRICE"), (b)
by delivery of shares of Common Stock held by the Holder having a Current Market
Price equal to the Aggregate Purchase Price or (c) to the extent permitted by
applicable law, the delivery of a notice to the Company that the Holder is
exercising the Warrant without payment of the Purchase Price by authorizing the
Company to deliver the number of shares of Warrant Stock issuable upon exercise
of the Warrant to be determined based upon the following formula:

         ((MP - WP) x WS)/MP =    the number of shares of Warrant Stock issuable
                                  upon exercise of this Warrant without payment
                                  of the Purchase Price

         WHERE:

                  MP =     Current Market Price

                  WP =     Current Warrant Price

                  WS =     The number of shares of Warrant Stock issuable upon
                           exercise of this Warrant (in whole or in part).

Such notice may be in the form of the Subscription set out at the end of this
Warrant. Upon receipt thereof, the Company shall, as promptly as practicable and
in any event within ten (10) Business Days thereafter, cause to be executed and
delivered to such holder a certificate or certificates representing the
aggregate number of fully paid and nonassessable shares of Warrant Stock
issuable upon such exercise.

                  The stock certificate or certificates for Warrant Stock so
delivered shall be endorsed with a legend in the form contained in Section 5 of
the Securities Purchase Agreement and shall be in such denominations as may be
specified in said notice and shall be registered in the name of such holder or
such other name or names as shall be designated in said notice. Such certificate
or certificates shall be deemed to have been issued and such holder or any other
Person so designated to be named therein shall be deemed to have become a holder
of record of such shares, including to the extent permitted by law the right to
vote such shares or to consent or to receive notice as a stockholder, as of the
time said notice is received by the Company as aforesaid.

                  Except as otherwise provided in Section 8 hereof, the Company
shall pay all expenses, transfer taxes and other charges payable in connection
with the preparation, issue and delivery of stock certificates under this
Section 2, except that, in case such stock certificates shall be registered in a
name or names other than the name of the holder of this Warrant, funds
sufficient to pay all stock transfer taxes which shall be payable upon the
issuance of such stock certificate or certificates shall be paid by the holder
hereof at the time of delivering the notice of exercise mentioned above.

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                  All shares of Warrant Stock issuable upon the exercise of this
Warrant shall be validly issued, fully paid and nonassessable, and free from all
liens and other encumbrances thereon.

                  The Company will not close its books against the transfer of
this Warrant or of any share of Warrant Stock in any manner which interferes
with the timely exercise of this Warrant. [With the consent of the holder of
this Warrant, the Company will from time to time take all such action as may be
necessary to assure that the par value per share of the unissued Common Stock
acquirable upon exercise of this Warrant is at all times equal to or less than
the Current Warrant Price per share of Common Stock then in effect.]

                  No fractional shares or scrip representing fractional shares
shall be issued upon the exercise of this Warrant. If the exercise of this
Warrant results in a required issuance of a fraction of a share, an amount equal
to such fraction multiplied by the Current Market Price per share of Common
Stock on the day of delivery of notice of exercise to the Company shall be paid
to the holder of this Warrant in cash by the Company.

         Section 3. Transfer, Division and Combination. Subject to Section 10,
this Warrant and all rights hereunder are transferable, in whole or in part, on
the books of the Company to be maintained for such purpose, upon surrender of
this Warrant at the office of the Company maintained for such purpose pursuant
to Section 16, together with a written assignment of this Warrant duly executed
by the holder hereof or its agent or attorney and payment of funds sufficient to
pay any stock transfer taxes payable upon the making of such transfer. Upon such
surrender and payment the Company shall, subject to Section 10, execute and
deliver a new Warrant or Warrants in the name of the assignee or assignees and
in the denominations specified in such instrument of assignment, and this
Warrant shall promptly be cancelled. If and when this Warrant is assigned in
blank (in case the restrictions on transferability in Section 10 shall have been
terminated), the Company may (but shall not be obliged to) treat the bearer
hereof as the absolute owner of this Warrant for all purposes and the Company
shall not be affected by any notice to the contrary. This Warrant, if properly
assigned in compliance with this Section 3 and Section 10, may be exercised by
an assignee for the purchase of shares of Common Stock without having a new
Warrant issued.

                  This Warrant may, subject to Section 10, be divided or
combined with other Warrants upon presentation at the aforesaid office of the
Company, together with a written notice specifying the names and denominations
in which new Warrants are to be issued, signed by the holder hereof or its agent
or attorney. Subject to compliance with the preceding paragraph and with Section
10, as to any transfer which may be involved in such division or combination,
the Company shall execute and deliver a new Warrant or Warrants in exchange for
the Warrant or Warrants to be divided or combined in accordance with such
notice.

                  The Company shall pay all expenses, taxes (other than income
taxes, if any, of the transferee) and other charges incurred by the Company in
the performance of its obligations in connection with the preparation, issue and
delivery of Warrants under this Section 3.

                  The Company agrees to maintain at its aforesaid office books
for the registration and transfer of the Warrants.

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         Section 4. Adjustment of Stock Unit. The number of shares of Common
Stock comprising a Stock Unit shall be subject to adjustment from time to time
as set forth in this Section 4 with respect to any fact or event described
herein occurring after the date hereof. The Company will not create any class of
Common Stock which carries any rights to dividends or assets differing in any
respect from the rights of the Common Stock on the date hereof. Anything
contained in this Section 4 notwithstanding, any adjustment made pursuant to any
provision of this Section 4 shall be made without duplication of an adjustment
otherwise required by and made pursuant to another provision of this Section 4
on account of the same facts or events.

                  A.       Stock Dividends, Subdivisions and Combinations. In
case at any time or from time to time the Company shall:

                           (1)      take a record of the holders of its Common
         Stock for the purpose of entitling them to receive a dividend payable
         in, or other distribution of, Common Stock, or

                           (2)      subdivide its outstanding shares of Common
         Stock into a larger number of shares of Common Stock, or

                           (3)      combine its outstanding shares of Common
         Stock into a smaller number of shares of Common Stock,

then the number of shares of Common Stock comprising a Stock Unit immediately
after the happening of any event described in clauses (1) through (3) above
shall be adjusted so as to consist of the number of shares of Common Stock which
a record holder of the number of shares of Common Stock constituting a Stock
Unit immediately prior to the happening of such event would own or be entitled
to receive after the happening of event described in clauses (1) through (3)
above.

                  B.       Certain Other Dividends and Distributions. In case at
any time or from time to time the Company shall take a record of the holders of
its Common Stock for the purpose of entitling them to receive any dividend or
other distribution of:

                           (1)      cash (other than a cash distribution made as
         a dividend and payable out of earnings or earned surplus legally
         available for the payment of dividends under the laws of the
         jurisdiction of incorporation of the Company, to the extent, but only
         to the extent, that the aggregate of all such dividends paid or
         declared after the date hereof, does not exceed the consolidated net
         income of the Company and its consolidated subsidiaries earned
         subsequent to the date hereof determined in accordance with generally
         accepted accounting principles), or

                           (2)      any evidence of its indebtedness (other than
         Convertible Securities), any shares of its stock (other than Additional
         Shares of Common Stock) or any other securities or property of any
         nature whatsoever (other than cash and other than Convertible
         Securities or Additional Shares of Common Stock), or

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                           (3)      any warrants, options or other rights to
         subscribe for or purchase (i) any evidences of its indebtedness (other
         than Convertible Securities), (ii) any shares of its stock (other than
         Additional Shares of Common Stock) or (iii) any other securities or
         property of any nature whatsoever (other than cash and other than
         Convertible Securities or Additional Shares of Common Stock),

then the number of shares of Common Stock thereafter comprising a Stock Unit
shall be adjusted to that number determined by multiplying the number of shares
of Common Stock comprising a Stock Unit immediately prior to such adjustment by
a fraction (i) the numerator of which shall be the Current Market Price per
share of Common Stock at the date of taking such record, and (ii) the
denominator of which shall be such Current Market Price per share of Common
Stock minus the portion applicable to one share of Common Stock of any such cash
so distributable (if any) and of the fair value of any and all such evidences of
indebtedness, shares of stock, other securities or property, or warrants,
options or other subscription or purchase rights, so distributable (if any).
Such fair value shall be determined in good faith by the Board of Directors of
the Company, provided that if such determination is objected to by the Holder,
such determination shall be made by an independent appraiser selected by such
Board of Directors and not objected to by the Holder. The fees and expenses of
such appraiser shall be paid by the Company. A reclassification (other than a
change in par value) of the Common Stock into shares of Common Stock and shares
of any other class of stock shall be deemed a distribution by the Company to the
holders of its Common Stock of such shares of such other class of stock within
the meaning of this Subsection and, if the outstanding shares of Common Stock
shall be changed into a larger or smaller number of shares of Common Stock as a
part of such reclassification, shall be deemed a subdivision or combination, as
the case may be, of the outstanding shares of Common Stock within the meaning of
Subsection A of this Section 4.

                  C.       Issuance of Additional Shares of Common Stock. In
case at any time or from time to time the Company shall (except as hereinafter
provided) issue, whether in connection with the merger of a corporation into the
Company or otherwise, any Additional Shares of Common Stock for a consideration
per share less than the Current Market Price per share of Common Stock, then the
number of shares of Common Stock thereafter comprising a Stock Unit shall be
adjusted to be that number determined by multiplying the number of shares of
Common Stock comprising a Stock Unit immediately prior to such adjustment by a
fraction (i) the numerator of which shall be the number of shares of Common
Stock outstanding, plus the number of such Additional Shares of Common Stock so
issued, and (ii) the denominator of which shall be the number of shares of
Common Stock outstanding, plus the number of shares of Common Stock which the
aggregate consideration for the total number of such Additional Shares of Common
Stock would purchase at the Current Market Price per share of Common Stock. For
purposes of this Subsection, the date as of which the Current Market Price per
share of Common Stock shall be computed shall be the earlier of (a) the date on
which the Company shall enter into a firm contract for the issuance of such
Additional Shares of Common Stock, or (b) the date of actual issuance of such
Additional Shares of Common Stock. The provisions of this Subsection shall not
apply to any issuance of Additional Shares of Common Stock for which an
adjustment is provided under Subsection A of this Section 4. No adjustment of
the number of shares of Common Stock comprising a Stock Unit shall be made under
this Subsection upon the issuance of any Additional Shares of Common Stock which
are issued pursuant to the exercise of any warrants, options or other
subscription or purchase rights or pursuant to the exercise of any

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conversion or exchange rights in any Convertible Securities, if any such
adjustment shall previously have been made upon the issuance of such warrants,
options or other rights or upon the issuance of such Convertible Securities (or
upon the issuance of any warrants, options or other rights therefor) pursuant to
Subsection D or E of this Section 4.

                  D.       Issuance of Warrants, Options or Other Rights. In
case at any time or from time to time the Company shall take a record of the
holders of its Common Stock for the purpose of entitling them to receive a
distribution of, or shall otherwise issue, any warrants, options or other rights
to subscribe for or purchase any Additional Shares of Common Stock or any
Convertible Securities and the consideration per share for which Additional
Shares of Common Stock may at any time thereafter be issuable pursuant to such
warrants, options or other rights or pursuant to the terms of such Convertible
Securities shall be less than the Current Market Price per share of Common
Stock, then the number of shares of Common Stock thereafter comprising a Stock
Unit shall be adjusted to be the number determined pursuant to the first
sentence of Subsection C of this Section 4. All adjustments made pursuant to
this Subsection D shall be made on the basis that (i) the maximum number of
Additional Shares of Common Stock issuable pursuant to all such warrants,
options or other rights or necessary to effect the conversion or exchange of all
such Convertible Securities shall be deemed to have been issued as of the date
specified in the last sentence of this Subsection, (ii) the aggregate
consideration for such maximum number of Additional Shares of Common Stock shall
be deemed to be the minimum consideration received and receivable by the Company
for the issuance of such Additional Shares of Common Stock pursuant to such
warrants, options or other rights or pursuant to the terms of such Convertible
Securities and (iii) the consideration per share received by the Company for
such Additional Shares of Common Stock shall be that number determined by
dividing (x) the aggregate consideration for such maximum number of Additional
Shares of Common Stock (determined as set forth in clause (ii) of this sentence)
by (y) the maximum number of Additional Shares of Common Stock issuable pursuant
to all such warrants, options or other rights or necessary to effect the
conversion or exchange of all such Convertible Securities (determined as set
forth in clause (i) of this sentence). For purposes of this Subsection, the
computation date for subclause (i) above and as of which the Current Market
Price per share of Common Stock shall be computed shall be the earliest of (a)
the date on which the Company shall take a record of the holders of its Common
Stock for the purpose of entitling them to receive any such warrants, options or
other rights, (b) the date on which the Company shall enter into a firm contract
for the issuance of such warrants, options or other rights, and (c) the date of
actual issuance of such warrants, options or other rights.

                  E.       Issuance of Convertible Securities. In case at any
time or from time to time the Company shall take a record of the holders of its
Common Stock for the purpose of entitling them to receive a distribution of, or
shall otherwise issue, any Convertible Securities and the consideration per
share for which Additional Shares of Common Stock may at any time thereafter be
issuable pursuant to the terms of such Convertible Securities shall be less than
the Current Market Price per share of Common Stock, then the number of shares of
Common Stock thereafter comprising a Stock Unit shall be adjusted to be the
number determined pursuant to the first sentence of Subsection C of this Section
4. All adjustments made pursuant to this Subsection E shall be made on the basis
that (i) the maximum number of Additional Shares of Common Stock necessary to
effect the conversion or exchange of all such Convertible Securities shall be
deemed to have been issued as of the computation date specified in the
penultimate

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sentence of this Subsection, (ii) the aggregate consideration for such maximum
number of Additional Shares of Common Stock shall be deemed to be the minimum
consideration received and receivable by the Company for the issuance of such
Additional Shares of Common Stock pursuant to the terms of such Convertible
Securities and (iii) the consideration per share received by the Company for
such Additional Shares of Common Stock shall be that number determined by
dividing (x) the aggregate consideration for such maximum number of Additional
Shares of Common Stock (determined as set forth in clause (ii) of this sentence)
by (y) the maximum number of Additional Shares of Common Stock necessary to
effect the conversion or exchange of all such Convertible Securities (determined
as set forth in clause (i) of this sentence). For purposes of this Subsection,
the computation date for clause (i) above and as of which the Current Market
Price per share of Common Stock shall be computed shall be the earliest of (a)
the date on which the Company shall take a record of the holders of its Common
Stock for the purpose of entitling them to receive any such Convertible
Securities, (b) the date on which the Company shall enter into a firm contract
for the issuance of such Convertible Securities, and (c) the date of actual
issuance of such Convertible Securities. No adjustment of the number of shares
of Common Stock comprising a Stock Unit shall be made under this Subsection upon
the issuance of any Convertible Securities which are issued pursuant to the
exercise of any warrants, options or other subscription or purchase rights
therefor, if any such adjustment shall previously have been made upon the
issuance of such warrants, options or other rights pursuant to Subsection D of
this Section 4.

                  F.       Superseding Adjustment of Stock Unit. If, at any time
after any adjustment of the number of shares of Common Stock comprising a Stock
Unit shall have been made pursuant to the foregoing Subsection D or E of this
Section 4 on the basis of the issuance of warrants, options or other rights or
the issuance of other Convertible Securities, or after any new adjustment of the
number of shares of Common Stock comprising a Stock Unit shall have been made
pursuant to this Subsection,

                           (1)      such warrants, options or rights or the
         right of conversion or exchange in such other Convertible Securities
         shall expire, and a portion or all of such warrants, options or rights,
         or the right of conversion or exchange in respect of a portion of such
         other Convertible Securities, as the case may be, shall not have been
         exercised, or

                           (2)      the consideration per share for which
         Additional Shares of Common Stock are issuable pursuant to such
         warrants, options or rights or the terms of such other Convertible
         Securities, shall be increased solely by virtue of provisions therein
         contained for an automatic increase in such consideration per share
         upon the arrival of a specified date or the happening of a specified
         event,

such previous adjustment shall be rescinded and annulled and the Additional
Shares of Common Stock which were deemed to have been issued by virtue of the
computation made in connection with the adjustment so rescinded and annulled
shall no longer be deemed to have been issued by virtue of such computation.
Thereupon, a recomputation shall be made of the effect of such warrants, options
or rights or other Convertible Securities on the basis of:

                           (3)      treating the number of Additional Shares of
         Common Stock, if any, theretofore actually issued or issuable pursuant
         to the previous exercise of such warrants,

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         options or rights or such right of conversion or exchange, as having
         been issued on the date or dates of such issuance as determined for
         purposes of such previous adjustment and for the consideration actually
         received and receivable therefor, and

                           (4)      treating any such warrants, options or
         rights or any such other Convertible Securities which then remain
         outstanding as having been granted or issued immediately after the time
         of such expiration or of such increase of the consideration per share
         for which such Additional Shares of Common Stock are issuable under
         such warrants, options or rights or other Convertible Securities,

and, if and to the extent called for by the foregoing provisions of this Section
4 on the basis aforesaid, a new adjustment of the number of shares of Common
Stock comprising a Stock Unit shall be made, which new adjustment shall
supersede the previous adjustment so rescinded and annulled.

                  G.       Other Provisions Applicable to Adjustments Under this
Section. The following provisions shall be applicable to the making of
adjustments of the number of shares of Common Stock comprising a Stock Unit
hereinbefore provided for in this Section 4:

                           (1)      Treasury Stock. The sale or other
         disposition of any issued shares of Common Stock owned or held by or
         for the account of the Company shall be deemed an issuance thereof for
         purposes of this Section 4.

                           (2)      Computation of Consideration. To the extent
         that any Additional Shares of Common Stock or any Convertible
         Securities or any warrants, options or other rights to subscribe for or
         purchase any Additional Shares of Common Stock or any Convertible
         Securities shall be issued solely for cash consideration, the
         consideration received by the Company therefor shall be deemed to be
         the amount of cash received by the Company therefor, or, if such
         Additional Shares of Common Stock or Convertible Securities are offered
         by the Company for subscription, the subscription price, or, if such
         Additional Shares of Common Stock or Convertible Securities are sold to
         underwriters or dealers for public offering without a subscription
         offering, the initial public offering price, in any such case excluding
         any amounts paid or receivable for accrued interest or accrued
         dividends and without deduction of any compensation, discounts or
         expenses paid or incurred by the Company for and in the underwriting
         of, or otherwise in connection with, the issue thereof. To the extent
         that such issuance shall be for a consideration other than solely for
         cash, then, except as herein otherwise expressly provided, the amount
         of such consideration shall be deemed to be the fair value of such
         consideration at the time of such issuance as determined in good faith
         by the Board of Directors of the Company, provided that if such
         determination is objected to by the Holder, such determination shall be
         made by an independent appraiser selected by such Board of Directors
         and not objected to by the Holder. The fees and expenses of such
         appraiser shall be paid by the Company. The consideration for any
         Additional Shares of Common Stock issuable pursuant to any warrants,
         options or other rights to subscribe for or purchase the same shall be
         the consideration received or receivable by the Company for issuing
         such warrant, options or other rights, plus the additional
         consideration payable to the Company upon the exercise of such
         warrants, options or other rights. The

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         consideration for any Additional Shares of Common Stock issuable
         pursuant to the terms of any Convertible Securities shall be the
         consideration received or receivable by the Company for issuing any
         warrants, options or other rights to subscribe for or purchase such
         Convertible Securities (if any), plus the consideration paid or payable
         to the Company in respect of the subscription for or purchase of such
         Convertible Securities, plus the additional consideration, if any,
         payable to the Company upon the exercise of the right of conversion or
         exchange in such Convertible Securities.

                           (3)      When Adjustments To Be Made. The adjustments
         required by the preceding Subsections of this Section 4 shall be made
         whenever and as often as any specified event requiring an adjustment
         shall occur. For the purpose of any adjustment, any specified event
         shall be deemed to have occurred at the close of business on the date
         of its occurrence.

                           (4)      Fractional Interests. In computing
         adjustments under this Section, fractional interests in Common Stock
         shall be taken into account to the nearest 1/100th of a share.

                           (5)      When Adjustment Not Required. If the Company
         shall take a record of the holders of its Common Stock for the purpose
         of entitling them to receive a dividend or distribution or subscription
         or purchase rights and shall, thereafter and before the distribution
         thereof to shareholders, legally abandon its plan to pay or deliver
         such dividend, distribution, subscription or purchase rights, then
         thereafter no adjustment shall be required by reason of the taking of
         such record and any such adjustment previously made in respect thereof
         shall be rescinded and annulled.

                  H.       Merger, Consolidation or Disposition of Assets. In
case the Company shall merge or consolidate into another corporation, or shall
sell, transfer or otherwise dispose of all or substantially all of its property,
assets or business to another corporation and pursuant to the terms of such
merger, consolidation or disposition, shares of common stock of the successor or
acquiring corporation are to be received by or distributed to the holders of
Common Stock of the Company, then the Holder shall have the right thereafter to
receive, upon exercise of this Warrant, Stock Units each comprising the number
of shares of common stock of the successor or acquiring corporation receivable
upon or as a result of such merger, consolidation or disposition of assets by a
holder of the number of shares of Common Stock comprising a Stock Unit
immediately prior to such event. If, pursuant to the terms of such merger,
consolidation or disposition of assets, any cash, shares of stock or other
securities or property of any nature whatsoever (including warrants, options or
other subscription or purchase rights) are to be received by or distributed to
the holders of Common Stock of the Company in addition to common stock of the
successor or acquiring corporation, there shall be either, at the Holder's
option, (i) an adjustment in the number of shares of Common Stock thereafter
comprising a Stock Unit to that number determined by multiplying the number of
shares of Common Stock comprising a Stock Unit immediately prior to such
adjustment by a fraction (x) the numerator of which shall be the Current Market
Price per share of Common Stock at the date of such merger, consolidation or
disposition, and (y) the denominator of which shall be such Current Market Price
per share minus the portion applicable to one share of Common Stock of any cash
so distributed and of the fair value of any and all such shares of stock,
securities or other property or

                                       11
<PAGE>   12

(ii) the Holder shall have the right to receive such cash, shares of stock or
other securities or property of any nature as a holder of the number of shares
of Common Stock underlying a Stock Unit would have been entitled to receive upon
the occurrence of such event, for each Stock Unit into which the Holder's
Warrants are exercisable. Such fair value shall be determined in good faith by
the Board of Directors of the Company, provided that if such determination is
objected to by the Holder, such determination shall be made by an independent
appraiser selected by such Board of Directors and not objected to by the Holder.
The fees and expenses of such appraiser shall be paid by the Company. In case of
any such merger, consolidation or disposition of assets, the successor or
acquiring corporation shall expressly assume the due and punctual observance and
performance of each and every covenant and condition of this Warrant and the
Securities Purchase Agreement to be performed and observed by the Company and
all of the obligations and liabilities hereunder and thereunder, subject to such
modification as shall be necessary to provide for adjustments of Stock Units
which shall be as nearly equivalent as practicable to the adjustments provided
for in this Section 4. For the purposes of this Section 4 "common stock of the
successor or acquiring corporation" shall include stock of such corporation of
any class, which is not preferred as to dividends or assets over any other class
of stock of such corporation and which is not subject to redemption, and shall
also include any evidences of indebtedness, shares of stock or other securities
which are convertible into or exchangeable for any such stock, either
immediately or upon the arrival of a specified date or the happening of a
specified event, and any warrants, options or other rights to subscribe for or
purchase any such stock. The foregoing provisions of this Subsection shall
similarly apply to successive mergers, consolidations or dispositions of assets.

                  I.       Other Action Affecting Common Stock. In case at any
time or from time to time the Company shall take any action affecting its Common
Stock, other than an action described in any of the foregoing Subsections A to
H, inclusive, of this Section 4 and the actions described in clauses (i) through
(vii) of the definition of Additional Shares of Common Stock, then, unless in
the reasonable opinion of the Board of Directors of the Company such action will
not have a materially adverse effect upon the rights of the Holder, the number
of shares of Common Stock or other stock comprising a Stock Unit, or the
purchase price thereof, shall be adjusted in such manner and at such time as the
Board of Directors of the Company may in good faith determine to be equitable in
the circumstances.

                  J.       No Adjustments for Certain Transactions. Anything
contained in this Warrant notwithstanding, the number of shares of Common Stock
comprising a Stock Unit and the Purchase Price per Stock Unit shall not be
adjusted, nor be subject to adjustment, on account of the granting of any rights
under a phantom stock plan, stock appreciation rights plan or other deferred
compensation plan to officers, directors or employees of the Company or its
affiliates, if (i) no shares of Common Stock are issued or required to be issued
under any such plan and (ii) the only consideration paid or payable to any
participant in such plan is cash.

         Section 5. Notice to Warrant Holders.

                  A.       Notice of Adjustment of Stock Unit or Purchase Price.
Whenever the number of shares of Warrant Stock comprising a Stock Unit or the
Purchase Price per Stock Unit shall be adjusted pursuant to Section 4, the
Company shall forthwith obtain a certificate signed by the president of the
Company and the principal financial officer of the Company, setting

                                       12
<PAGE>   13

forth, in reasonable detail, the event requiring the adjustment and the method
by which such adjustment was calculated (including a statement of the fair
value, as determined by the Board of Directors of the Company, of any evidences
of indebtedness, shares of stock, other securities or property or warrants,
options or other subscription or purchase rights referred to in Section 4.B,
Section 4.G(2) or Section 4.H) and specifying the number of shares of Common
Stock comprising a Stock Unit and (if such adjustment was made pursuant to
Section 4.H or Section 4.I) describing the number and kind of any other shares
of stock comprising a Stock Unit, and any change in the Purchase Price thereof
after giving effect to such adjustment or change. The Company shall promptly,
and in any case within 10 days after the making of such adjustment, cause a
signed copy of such certificate to be delivered to the Holder. The Company shall
keep at its office or agency, maintained for the purpose pursuant to Section 16,
copies of all such certificates and cause the same to be available for
inspection at said office during normal business hours by the Holder or any
prospective purchaser of the Warrant designated by the Holder.

                  B.       Notice of Certain Corporate Action. In case the
Company shall propose (a) to pay any dividend payable in cash or in stock of any
class to the holders of its Common Stock or to make any other distribution to
the holders of its Common Stock, or (b) to offer to the holders of its Common
Stock rights to subscribe for or to purchase any Additional Shares of Common
Stock or shares of stock of any class or any other securities, rights or
options, or (c) to effect any reclassification of its Common Stock (other than a
reclassification involving only the subdivision or combination of outstanding
shares of Common Stock), or (d) to effect any capital reorganization, or (e) to
effect any consolidation, merger or sale, change to the Company's charter or
bylaws, transfer or other disposition of all or substantially all of its
property, assets or business, or (f) to effect the liquidation, dissolution or
winding up of the Company, then in each such case, the Company shall give to
each holder of a Warrant, in accordance with Section 17, a notice, certified by
the president of the Company and the principal financial officer of the Company,
of such proposed action, which shall specify the date on which a record is to be
taken for the purposes of such stock dividend, distribution or rights, or the
date on which such reclassification, reorganization, consolidation, merger,
sale, change to the Company's charter or bylaws, transfer, disposition,
liquidation, dissolution, or winding up is to take place and the date of
participation therein by the holders of Common Stock, if any such date is to be
fixed, and shall also set forth such facts with respect thereto as shall be
reasonably necessary to indicate the effect of such action on the Common Stock
and the number and kind of any other shares of stock which will comprise a Stock
Unit, and the purchase price or prices thereof, after giving effect to any
adjustment which will be required as a result of such action. Such notice shall
be so given in the case of any action covered by clause (a) or (b) above at
least twenty days prior to the record date for determining holders of the Common
Stock for purposes of such action, and in the case of any other such action, at
least thirty days prior to the date of the taking of such proposed action or the
date of participation therein by the holders of Common Stock, whichever shall be
the earlier.

         Section 6. Reservation and Authorization of Common Stock; Registration
with or Approval of any Governmental Authority. The Company shall at all times
reserve and keep available for issue upon the exercise of Warrants such number
of its authorized but unissued shares of Common Stock as will be sufficient to
permit the exercise in full of all outstanding Warrants. Without the prior
written consent of the Holder, the Company will not amend its

                                       13
<PAGE>   14

Certificate of Incorporation in any respect relating to the Common Stock other
than to increase or decrease the number of shares of authorized capital stock
(subject to the provisions of the preceding sentence) or to decrease the par
value of Common Stock.

                  Before taking any action which would cause an adjustment
reducing the Current Warrant Price per share of Common Stock below the then par
value, if any, of the shares of Common Stock issuable upon exercise of the
Warrants, the Company shall take any corporate action which may, in the opinion
of its counsel, be necessary in order that the Company may validly and legally
issue fully-paid and nonassessable shares of Common Stock at such adjusted
Current Warrant Price.

                  Before taking any action which would result in an adjustment
in the number of shares of Common Stock comprising a Stock Unit or in the
Current Warrant Price per share of Common Stock, the Company shall obtain all
such authorizations or exemptions thereof, or consents thereto, as may be
necessary from any public regulatory body or bodies having jurisdiction thereof
(except that nothing contained in this Warrant certificate shall require the
Company to register the Warrants under the Securities Act or any similar federal
or state equivalent).

         Section 7. Taking of Record; Stock and Warrant Transfer Books. In the
case of all dividends or other distributions by the Company to the holders of
its Common Stock with respect to which any provision of Section 4 refers to the
taking of a record of such holders, the Company will in each such case take such
a record and will take such record as of the close of business on a Business
Day. The Company will not at any time, except (i) upon dissolution, liquidation
or winding up, or (ii) for purposes of declaring and paying a dividend or
matters related to voting by shareholders of the Company, close its stock
transfer books or Warrant transfer books so as to result in preventing or
delaying the exercise or transfer of any Warrant.

         Section 8. Transfer Taxes. The Company will pay any and all transfer
taxes that may be payable in respect of the issuance or delivery of shares of
Common Stock on exercise of this Warrant. The Company shall not, however, be
required to pay any tax which may be payable in respect of any transfer involved
in the issue and delivery of shares of Common Stock in a name other than that in
which this Warrant is registered, and no such issue or delivery shall be made
unless and until the person requesting such issue has paid to the Company the
amount of any such tax, or has established, to the satisfaction of the Company,
that such tax has been paid.

         Section 9. No Voting Rights. This Warrant shall not entitle the holder
hereof to any voting rights, or to any rights as a stockholder of the Company.

         Section 10. Restrictions on Transferability. The Warrants and the
Warrant Stock shall be transferable only (i) in accordance with the provisions
of Section 5 of the Securities Purchase Agreement and (ii) upon compliance with
the conditions specified in this Warrant and in compliance with the provisions
of the Securities Act and applicable state securities laws in respect of the
transfer of any Warrant or any Warrant Stock, and any holder of this Warrant
shall be bound by the provisions of (and entitled to the benefits of) Section 3
hereof.

                                       14
<PAGE>   15

         Section 11. Limitation of Liability. No provision hereof, in the
absence of affirmative action by the holder hereof to purchase shares of Common
Stock, and no mere enumeration herein of the rights or privileges of the holder
hereof, shall give rise to any liability of such holder for the purchase price
or as a stockholder of the Company, whether such liability is asserted by the
Company or by creditors of the Company.

         Section 12. Registration Rights. The Holder shall have registration
rights and benefits with respect to any Warrant Stock issuable upon the exercise
hereof identical to the rights and benefits (and subject to the same terms and
conditions) as those set forth in Section 7 of the Securities Purchase Agreement
as if such provisions were set forth herein in their entirety. Nothing in this
Section 12 shall limit or reduce the rights and benefits of the Purchaser under
the Securities Purchase Agreement.

         Section 13. Loss, Destruction of Warrant Certificates. Upon receipt of
evidence satisfactory to the Company of the loss, theft, destruction or
mutilation of this Warrant and, in the case of any such loss, theft or
destruction, upon receipt of indemnity or security satisfactory to the Company
(the original Holder's or any other institutional holder's indemnity being
satisfactory indemnity in the event of loss, theft or destruction of any Warrant
owned by such institutional holder), or, in the case of any such mutilation,
upon surrender and cancellation of such Warrant, the Company will make and
deliver, in lieu of such lost, stolen, destroyed or mutilated Warrant, a new
Warrant of like tenor and representing the right to purchase the same aggregate
number of shares of Common Stock.

         Section 14. Furnish Information. The Company agrees that it shall
deliver to the holder of record hereof promptly after their becoming available
copies of all financial statements, reports and proxy statements which the
Company shall have sent to its stockholders generally.

         Section 15. Amendments. The terms of this Warrant may be amended, and
the observance of any term therein may be waived, only with the written consent
of the Holder.

         Section 16. Office of the Company. So long as any of the Warrants
remains outstanding, the Company shall maintain an office in Houston, Texas
where the Warrants may be presented for exercise, transfer, division or
combination as in this Warrant provided. Such office shall be at 3700 Buffalo
Speedway, Suite 960 unless and until the Company shall designate and maintain
some other office for such purposes and give written notice thereof to the
Holder.

         Section 17. Notices Generally. All notices, requests and other
communications hereunder must be in writing and will be deemed to have been duly
given only if delivered personally or by facsimile transmission or mailed (first
class postage prepaid) to the parties at the following addresses or facsimile
numbers:

                                       15
<PAGE>   16

                  If to Company, to:

                     Contango Oil and Gas Company
                     3700 Buffalo Speedway, Suite 960
                     Houston, Texas  77098
                     Attention:  Kenneth R. Peak, President and
                                 Chief Executive Officer
                     Phone:      (713) 960-1901
                     Fax:        (713) 960-1065

                     with a copy to:

                     Morgan, Lewis & Bockius LLP
                     300 South Grand Avenue, 22nd Floor
                     Los Angeles, California 90071
                     Attention:  Richard A. Shortz, Esq.
                     Phone:         (213) 612-2500
                     Fax:           (213) 612-2554

                  If to Sellers, to:

                        with a copy to:

                  All such notices, requests and other communications will (i)
if delivered personally to the address as provided in this Section, be deemed
given upon delivery, (ii) if delivered by facsimile transmission to the
facsimile number as provided in this Section, be deemed given upon receipt, and
(iii) if delivered by mail in the manner described above to the address as
provided in this Section, be deemed given upon receipt (in each case regardless
of whether such notice, request or other communication is received by any other
Person to whom a copy of such notice is to be delivered pursuant to this
Section). Any party from time to time may change its address, facsimile number
or other information for the purpose of notices to that party by giving notice
specifying such change to the other party hereto.

         Section 18. Governing Law. THIS WARRANT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF NEVADA.

                                       16
<PAGE>   17

                  IN WITNESS WHEREOF, the Company has caused this Certificate to
be signed in its name by its President and Chief Executive Officer, such
signature to be attested to by the Company's Secretary or Assistant Secretary,
and the Company's corporate seal to be impressed hereon.

Dated:  December 29, 1999

[SEAL]                         CONTANGO OIL & GAS COMPANY,
                               a Nevada corporation

                                    By: /s/ KENNETH R. PEAK
                                        ---------------------------------------
                                          Kenneth R. Peak
                                          President and Chief Executive Officer

                                       17
<PAGE>   18

SUBSCRIPTION FORM

                                  (to be executed only upon exercise of Warrant)

                  The undersigned registered owner of this Warrant irrevocably
exercises this Warrant for and purchases ___________ Stock Units of
___________________, a __________ corporation, purchasable with this Warrant,
herewith makes payment therefor on the terms and conditions specified in this
Warrant and requests that certificates for the shares of Common Stock hereby
purchased (and any securities or other property issuable upon such exercise) be
issued in the name of and delivered to ______________________ whose address is
_________________________________.

Dated:

                              --------------------------------------------------
                              (Signature of Registered Owner)

                              --------------------------------------------------
                              (Street Address)

                              --------------------------------------------------
                              (City)                (State)           (Zip Code)

                                       18
<PAGE>   19

                                 ASSIGNMENT FORM

                  FOR VALUE RECEIVED the undersigned registered owner of this
Warrant hereby sells, assigns and transfers unto the assignee named below all of
the rights of the undersigned under this Warrant, with respect to the number of
Stock Units set forth below:

<TABLE>
<CAPTION>
                                                                  No. of Stock
    Name and Address of Assignee                                      Units
    ----------------------------                                  ------------
<S>                                                               <C>

</TABLE>

and does hereby irrevocably constitute and appoint _____________________
attorney to make sure transfer on the books of ________________, a ___________
corporation, maintained for the purpose, with full power of substitution in the
premises.

Dated:

                              --------------------------------------------------
                              Signature

                              --------------------------------------------------
                              Witness

NOTICE:           The signature to the assignment must correspond with the name
                  as written upon the face of the within Warrant in every
                  particular, without alteration or enlargement or any change
                  whatever.

                  [The signature to this assignment must be guaranteed by an
                  Eligible Guarantor Institution as defined in Rule 17Ad-15
                  promulgated under the Securities Exchange Act of 1934, as
                  amended, or any successor thereto.]

                                       19<PAGE>   1

                                                                    EXHIBIT 10.5

                           CONTANGO OIL & GAS COMPANY
                                CO-SALE AGREEMENT

         THIS CO-SALE AGREEMENT (the "Agreement") is made as of this 29th day of
December, 1999, by and among Contango Oil & Gas Company, a Nevada corporation
(the "Company"), Trust Company of the West, a California trust company, in its
capacities as Investment Manager pursuant to the Investment Management Agreement
dated as of June 6, 1988 between General Mills, Inc. and the Trust Company of
the West and as Custodian pursuant to the Custody Agreement dated as of February
6, 1989 among General Mills, Inc., the Trust Company of the West and State
Street Bank and Trust Company, as Trustee ("TCW"), and Kenneth R. Peak ("Peak").

                                    RECITALS

         WHEREAS, TCW is purchasing shares of the Company's Common Stock, and a
warrant to purchase additional shares of Common Stock (the "Warrant" and
together with the Common Stock purchased by TCW, the "Securities"), pursuant to
that certain Securities Purchase Agreement dated as of the date hereof (the
"Securities Purchase Agreement"), between TCW and the Company;

         WHEREAS, TCW was induced by the Company to purchase the Securities in
part by the Company's and Peak's agreement to enter into this Agreement; and

         WHEREAS, the parties desire to enter into this Agreement in order to
grant rights of co-sale to TCW.

         In consideration of the mutual covenants set forth herein, the parties
agree hereto as follows:

1. DEFINITIONS.

         (a) "CO-SALE STOCK" shall mean shares of the Company's Common Stock now
owned or subsequently acquired by Peak.

         (b) "COMMON STOCK" shall mean the Company's Common Stock and shares of
Common Stock issued or issuable upon exercise of the Warrant.

2. SALES BY PEAK.

         (a) If Peak proposes to sell or transfer any shares of Co-Sale Stock,
then Peak shall promptly give written notice (the "Notice") simultaneously to
the Company and to TCW at least thirty (30) days prior to the closing of such
sale or transfer. The Notice shall describe in reasonable detail the proposed
sale or transfer including, without limitation, the number of shares of Co-Sale
Stock to be sold or transferred, the nature of such sale or transfer, the
consideration to be paid, and the name and address of each prospective purchaser
or transferee.

<PAGE>   2

         (b) TCW shall have the right, exercisable upon written notice to Peak
within fifteen (15) days after the Notice, to participate in such sale of
Co-Sale Stock on the same terms and conditions. Such notice shall indicate the
number of shares of Common Stock TCW wishes to sell under its right to
participate. To the extent TCW exercises such right of participation in
accordance with the terms and conditions set forth below, the number of shares
of Co-Sale Stock that Peak may sell in the transaction shall be correspondingly
reduced.

         (c) TCW may sell all or any part of that number of shares equal to the
product obtained by multiplying (i) the aggregate number of shares of Co-Sale
Stock covered by the Notice by (ii) a fraction the numerator of which is the
number of shares of Common Stock owned by TCW at the time of the sale or
transfer and the denominator of which is the total number of shares of Common
Stock owned by Peak and TCW at the time of the sale or transfer. TCW shall
effect its participation in the sale by promptly delivering to Peak for transfer
to the prospective purchaser one or more certificates, properly endorsed for
transfer, which represent the number of shares of Common Stock which TCW elects
to sell.

         (d) The stock certificate or certificates that TCW delivers to Peak
pursuant to Section 2(c) shall be transferred to the prospective purchaser in
consummation of the sale of the Common Stock pursuant to the terms and
conditions specified in the Notice, and Peak shall concurrently therewith remit
to TCW that portion of the sale proceeds to which TCW is entitled by reason of
its participation in such sale. To the extent that any prospective purchaser or
purchasers prohibits such assignment or otherwise refuses to purchase shares or
other securities from TCW exercising its rights of co-sale hereunder, Peak shall
not sell to such prospective purchaser or purchasers any Co-Sale Stock unless
and until, simultaneously with such sale, Peak shall purchase such shares or
other securities from TCW on the same terms and conditions specified in the
Notice.

         (e) The exercise or non-exercise of the rights of TCW hereunder to
participate in one or more sales of Co-Sale Stock made by Peak shall not
adversely affect its rights to participate in subsequent sales of Co-Sale Stock
subject to Section 2(a).

         (i) If TCW does not elect to participate in the sale of the Co-Sale
Stock subject to the Notice, Peak may, not later than sixty (60) days following
delivery to the Company of the Notice, enter into an agreement providing for the
closing of the transfer of the Co-Sale Stock covered by the Notice within thirty
(30) days of such agreement on terms and conditions not more materially
favorable to the transferor than those described in the Notice. Any proposed
transfer on terms and conditions materially more favorable than those described
in the Notice, as well as any subsequent proposed transfer of any of the Co-Sale
Stock by Peak, shall again be subject to the co-sale rights of TCW and shall
require compliance by Peak with the procedures described in this Section 2.

3. EXEMPT TRANSFERS.

         (a) Notwithstanding the foregoing, the co-sale rights of TCW shall not
apply to (i) any pledge of Co-Sale Stock made pursuant to a bona fide loan
transaction with a financial institution that creates a mere security interest,
(ii) any transfer to the ancestors, descendants or spouse of Peak or to trusts
for the benefit of such persons, (iii) any transfer or transfers by Peak to John

                                       2
<PAGE>   3

Jurrius so long as such transfer is made in connection with Jurrius' appointment
to the Company's Board of Directors, or (iv) any bona fide gift; provided that
in the event of any transfer made pursuant to one of the exemptions provided by
clauses (i), (ii) and (iv), (A) Peak shall inform TCW of such pledge, transfer
or gift prior to effecting it and (B) the pledgee, transferee or donee shall
furnish TCW with a written agreement to be bound by and comply with all
provisions of Section 2. Except with respect to Co-Sale Stock transferred under
clause (iii) above (which Co-Sale Stock shall no longer be subject to the
co-sale rights of TCW), such transferred Co-Sale Stock shall remain "Co-Sale
Stock" hereunder, and such pledgee, transferee or donee shall be treated
similarly with Peak for purposes of this Agreement.

         (b) Notwithstanding the foregoing, the provisions of Section 2 shall
not apply to the sale of any Co-Sale Stock to (i) the public pursuant to a
registration statement filed with, and declared effective by, the Securities and
Exchange Commission under the Securities Act of 1933, as amended (the
"Securities Act") or (ii) to the Company.

4. LEGEND.

         (a) Each certificate representing shares of Co-Sale Stock now or
hereafter owned by Peak or issued to any person in connection with a transfer
pursuant to Section 3(a) hereof shall be endorsed with the following legend:

         "THE SALE, PLEDGE, HYPOTHECATION OR TRANSFER OF THE SECURITIES
REPRESENTED BY THIS CERTIFICATE IS SUBJECT TO THE TERMS AND CONDITIONS OF A
CERTAIN CO-SALE AGREEMENT BY AND BETWEEN TCW, THE COMPANY AND CERTAIN HOLDERS OF
STOCK OF THE COMPANY. COPIES OF SUCH AGREEMENT MAY BE OBTAINED UPON WRITTEN
REQUEST TO THE SECRETARY OF THE COMPANY."

         (b) Peak agrees that the Company may instruct its transfer agent to
impose transfer restrictions on the shares represented by certificates bearing
the legend referred to in Section 4(a) above to enforce the provisions of this
Agreement and the Company agrees to promptly do so. The legend shall be removed
upon termination of this Agreement.

5. MISCELLANEOUS.

         (a) CONDITIONS TO EXERCISE OF RIGHTS. Exercise of TCW's rights under
this Agreement shall be subject to and conditioned upon, and Peak and the
Company shall use their best efforts to assist TCW in, compliance with
applicable laws.

         (b) GOVERNING LAW. This Agreement shall be governed by and construed
under the laws of the State of Nevada.

         (c) AMENDMENT. Any provision of this Agreement may be amended and the
observance thereof may be waived (either generally or in a particular instance
and either retroactively or prospectively), only by the written consent of (i)
as to the Company, only by the Company, (ii) as to TCW, only by TCW and (iii) as
to Peak, only by Peak.

                                       3

<PAGE>   4

         (d) TERM. This Agreement shall terminate upon the closing of a firm
commitment underwritten public offering of the Company's Common Stock pursuant
to an effective registration statement under the Securities Act.

         (e) NOTICES. All notices required or permitted hereunder shall be in
writing and shall be deemed effectively given: (i) upon personal delivery to the
party to be notified, (ii) when sent by confirmed telex or facsimile if sent
during normal business hours of the recipient; if not, then on the next business
day, (iii) five (5) days after having been sent by registered or certified mail,
return receipt requested, postage prepaid, or (iv) one (1) day after deposit
with a nationally recognized overnight courier, specifying next day delivery,
with written verification of receipt. All communications shall be sent to the
party to be notified at the address as set forth on the signature page hereof or
at such other address as such party may designate by ten (10) days advance
written notice to the other parties hereto.

         (f) SEVERABILITY. In the event one or more of the provisions of this
Agreement should, for any reason, be held to be invalid, illegal or
unenforceable in any respect, such invalidity, illegality, or unenforceability
shall not affect any other provisions of this Agreement, and this Agreement
shall be construed as if such invalid, illegal or unenforceable provision had
never been contained herein.

         (f) ATTORNEYS' FEES. In the event that any dispute among the parties to
this Agreement should result in litigation, the prevailing party in such dispute
shall be entitled to recover from the losing party all fees, costs and expenses
of enforcing any right of such prevailing party under or with respect to this
Agreement, including without limitation, such reasonable fees and expenses of
attorneys and accountants, which shall include, without limitation, all fees,
costs and expenses of appeals.

         (h) ENTIRE AGREEMENT. This Agreement constitutes the entire agreement
between the parties relative to the specific subject matter hereof. Any previous
agreement among the parties relative to the specific subject matter hereof is
superseded by this Agreement. This Agreement and the rights and obligations of
the parties hereunder shall inure to the benefit of, and be binding upon, their
respective successors, assigns and legal representatives.

         (i) COUNTERPARTS. This Agreement may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

                      [THIS SPACE INTENTIONALLY LEFT BLANK]

                                       4
<PAGE>   5

         IN WITNESS WHEREOF, the undersigned have executed this CO-SALE
AGREEMENT as of the date set forth above.

Company:                                 CONTANGO OIL & GAS COMPANY
                                         a Nevada corporation

                                         By: /s/ KENNETH R. PEAK
                                             -----------------------------------
                                             Kenneth R. Peak
                                             President and Chief Executive
                                               Officer

Peak:                                    /s/ KENNETH R. PEAK
                                         ---------------------------------------
                                         Kenneth R. Peak

TCW:                                     TRUST COMPANY OF THE WEST,

                                         a California trust company, in its
                                         capacities as Investment Manager
                                         pursuant to the Investment Management
                                         Agreement dated as of June 6, 1988
                                         between General Mills, Inc. and the
                                         Trust Company of the West and as
                                         Custodian pursuant to the Custody
                                         Agreement dated as of February 6, 1989
                                         among General Mills, Inc., the Trust
                                         Company of the West and State Street
                                         Bank and Trust Company, as trustee

                                         By: /s/ ARTHUR R. CARLSON
                                             -----------------------------------
                                             Arthur R. Carlson
                                             Managing Director

                                         By: /s/ THOMAS F. MEHLBERG
                                             -----------------------------------
                                             Thomas F. Mehlberg
                                             Senior Vice President

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