<PAGE>

                                                                    Exhibit 10.3

THE SECURITIES TO WHICH THIS AGREEMENT RELATES HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR UNDER ANY
STATE SECURITIES LAWS ("STATE LAWS") AND MAY NOT BE OFFERED, SOLD OR OTHERWISE
TRANSFERRED UNLESS THE OFFER AND SALE IS REGISTERED UNDER THE SECURITIES ACT OR
THE ISSUER RECEIVES AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE ISSUER
THAT THE OFFER AND SALE IS EXEMPT FROM SECURITIES ACT REGISTRATION.

                          SECURITIES PURCHASE AGREEMENT

     This agreement is made and entered into as of the 29th day of December,
1999, by and between Contango Oil & Gas Company (the "Issuer") and 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 (the "Purchaser").

      1.  Agreement to Purchase Securities. On the terms and subject to the
          --------------------------------
conditions set forth in this agreement, the Purchaser hereby agrees to purchase
from the Issuer 3,703,704 shares of the Issuer's common stock (the "Shares") and
warrants to purchase an additional 370,370 shares of common stock in the form
attached hereto as Exhibit A (the "Warrant") for an aggregate purchase price of
$2,540,000 (the "Purchase Price"), payable by wire transfer to the account of
the Issuer. The shares of Issuer's common stock that may be issued upon exercise
of the Warrant are referred to herein as the "Warrant Shares" and the Shares,
the Warrant and the Warrant Shares are collectively referred to herein as the
"Securities").

     2.   Wire Transfer of Payment for and Delivery of the Securities.
          -----------------------------------------------------------
Immediately after the Purchaser has wired the Purchase Price for the Securities
as instructed by Issuer, the Issuer shall issue and deliver a certificate
representing the Shares, and the Warrant in the form attached hereto as Exhibit
A, in the name and to the address specified by the Purchaser in the registration
and delivery instructions on the signature page of this agreement.

     3.   Purchaser's Representations and Warranties. The Purchaser hereby
          ------------------------------------------
represents and warrants to the Issuer that:

          3.1  Investment Intent. The Purchaser is acquiring the Securities
               -----------------
solely for the Purchaser's own account for investment purposes, and not with a
view to, or for offer or sale in connection with, any distribution of the
Securities in violation of the Securities Act.

          3.2  Access to Information. The Purchaser has received a copy of the
               ---------------------
Issuer's annual report on Form 10-KSB for the year ended June 30, 1999 (the
"Annual Report") and quarterly report on Form 10-QSB for the quarter ended
September 30, 1999 (the "Quarterly Report") and has reviewed them carefully,
including the risk factors set forth under the heading, "Management's Discussion
and Analysis or Plan of Operation -- Risk Factors." In addition, the Purchaser
has received and reviewed a copy of the Issuer's proxy statement for its annual
meeting of stockholders held on September 28, 1999 (the "Proxy Statement"). If
desired, the

<PAGE>

Purchaser has also sought and obtained from management of the Issuer such
additional information concerning the business, management and financial affairs
of the Issuer as the Purchaser has deemed necessary or appropriate in evaluating
an investment in the Issuer and determining whether or not to purchase the
Securities.

          3.3  Accredited Investor. By completing the Accredited Investor
               -------------------
Certification attached as Exhibit A, the Purchaser represents and warrants that
it is an accredited investor, as defined by Rule 501(a) of Regulation D under
the Securities Act.

          3.4  Preexisting Relationship; Knowledge and Experience. The Purchaser
               --------------------------------------------------
has a preexisting business relationship with certain of the Issuer's officers,
directors and/or controlling persons, is experienced in evaluating and investing
in the securities of businesses in the development stage, and has such knowledge
and experience in financial and business matters that it is capable of
evaluating the merits and risks of an investment in the Securities and of
protecting its interests in connection with an acquisition of the Securities.

          3.5  Suitability. The Purchaser has carefully considered, and has, to
               -----------
the extent the Purchaser deems it necessary, discussed with the Purchaser's own
professional legal, tax and financial advisers the suitability of an investment
in the Securities for the Purchaser's particular tax and financial situation,
and the Purchaser has determined that the Securities are a suitable investment
for the Purchaser.

          3.6  Ability to Bear Risk of Loss. The Purchaser is financially able
               ----------------------------
to hold the Securities subject to restrictions on transfer for an indefinite
period of time, and is capable of bearing the economic risk of losing up to the
entire amount of its investment in the Securities.

          3.7  Private Offering. The offer of the Securities was directly
               ----------------
communicated to the Purchaser by the Issuer. At no time was the Purchaser
presented with or solicited by any leaflet, newspaper or magazine article, radio
or television advertisement, or any other form of general advertising or
solicited or invited to attend a promotional meeting otherwise than in
connection and concurrently with such directly communicated offer.

          3.8  Truth and Accuracy. All representations and warranties made by
               ------------------
the Purchaser in this agreement are true and accurate as of the date hereof and
shall be true and accurate as of the date the Issuer issues the Securities. If
at any time prior to the issuance of the Securities any representation or
warranty shall not be true and accurate in any respect, the Purchaser shall so
notify the Issuer.

          3.9  Authority. The individuals executing and delivering this
               ---------
agreement on behalf of the Purchaser have been duly authorized to execute and
deliver this agreement on behalf of the Purchaser, the signature of both such
individuals is binding upon the Purchaser, the Purchaser is duly organized and
subsisting under the laws of the jurisdiction in which is was organized, and the
Purchaser was not formed for the specific purpose of acquiring the Securities.

          3.10 No Violation. The execution and delivery of this agreement and
               ------------
the consummation of the transactions or performance of the obligations
contemplated by this agreement do not and will not violate any term of the
Purchaser's organizational documents.

<PAGE>

          3.11 Enforceability. The Purchaser has duly executed and delivered
               --------------
this agreement and (subject to its execution by the Issuer) it constitutes a
valid and binding agreement of the Purchaser enforceable in accordance with its
terms against the Purchaser, except as such enforceability may be limited by
principles of public policy, and subject to laws of general application relating
to bankruptcy, insolvency and the relief of debtors and rules of law governing
specific performance, injunctive relief or other equitable remedies.

          3.12 Reliance on Own Advisers. In connection with the Purchaser's
               ------------------------
investment in the Securities, the Purchaser has not relied upon the Issuer or
its advisers for legal or tax advice, and has, if desired, in all cases sought
the advice of the Purchaser's own legal counsel and tax advisers.

          3.13 Scope of Business. The Purchaser has been advised and understands
               -----------------
that the Issuer will be exposed to numerous investment opportunities in all
areas of the oil and gas industry and may therefore pursue various types of
opportunities, even if they do not fit within the primary focus of the Issuer's
current business plan. For example, such opportunities could include investments
both onshore and offshore United States investments and also international
investments. Potential opportunities could also include such things as
downstream investments in oil and gas service companies, pipelines, and gas
processing and gas storage facilities.

     4.   Issuer's Representations and Warranties. The Issuer hereby represents
          ---------------------------------------
and warrants to the Purchaser that:

          4.1  Corporate Existence; Authority. The Issuer is a corporation duly
               ------------------------------
organized, validly existing and in good standing under the laws of Nevada, and
it has all requisite power and authority to carry on its business as it is being
conducted. The individual executing and delivering this agreement on behalf of
the Issuer has been duly authorized to execute and deliver this agreement on
behalf of the Issuer, the signature of such individual is binding upon the
Issuer.

          4.2  Enforceability. The Issuer has duly executed and delivered this
               --------------
agreement and (subject to its execution by the Purchaser) it constitutes a valid
and binding agreement of the Issuer enforceable in accordance with its terms
against the Issuer, except as such enforceability may be limited by principles
of public policy, and subject to laws of general application relating to
bankruptcy, insolvency and the relief of debtors and rules of law governing
specific performance, injunctive relief or other equitable remedies.

          4.3  Capitalization. (a) The Issuer has no outstanding capital stock
               --------------
other than common stock as of the date of this agreement. The Issuer is
authorized to issue 50,000,000 shares of common stock, of which (prior to giving
effect to the transactions set forth herein) 12,253,625 shares are issued and
outstanding, and 125,000 shares of preferred stock, none of which are issued and
outstanding. All of the outstanding shares of common stock of the Issuer have
been duly and validly issued and are fully paid, non-assessable and not subject
to any preemptive or similar rights. The Shares have been duly authorized and
when issued and delivered to the Purchaser against payment therefor as provided
by this agreement, will be validly issued, fully paid and non-assessable, and
the issuance of such Shares will not be subject to any preemptive or similar
rights. If and when issued, the Warrant Shares will have been duly authorized
and when issued and delivered to the Purchaser against payment therefor as
provided

<PAGE>

by in the Warrant, will be validly issued, fully paid and non-assessable, and
the issuance of such Warrant Shares will not be subject to any preemptive or
similar rights.

               (b)  Prior to giving effect to the transactions set forth herein,
there are no outstanding subscriptions, options, warrants, convertible
securities, calls, commitments, agreements or rights to purchase or otherwise
acquire from the Issuer any shares of, or any securities convertible into, the
capital stock of the Issuer except as set forth on Schedule 4.3(b), including
                                                   ---------------
(i) outstanding options to purchase 418,667 shares of the Issuer's common stock
under the Issuer's 1999 Stock Incentive Plan, under which 5,000,000 shares of
common stock are reserved for issuance, (ii) warrants exercisable for 2,460,000
shares of the Issuer's common stock at the exercise price of $1.00 per share,
and (iii) subscriptions to purchase an aggregate of 850,666 shares of the
Issuer's common stock at a per share purchase price of $0.75. In addition, as of
the date of this Agreement the Issuer has committed to grant (but has not yet
granted) options to purchase an additional 97,167 shares of its common stock
under its 1999 Stock Incentive Plan.

               (c)  Except as set forth on Schedule 4.3(c), no shareholders of
                                           ---------------
the Issuer have any right to require the registration of any securities of the
Issuer or to participate in any such registration.

          4.4  No Conflicts. The issuance and sale of the Securities to the
               ------------
Purchaser as contemplated hereby and the performance of this Agreement, the
Warrant and the Co-Sale Agreement by the Issuer and Peak (as defined in the
Co-Sale Agreement) will not violate or conflict with the Issuer's Articles of
Incorporation or By-laws or any agreements to which the Issuer is a party or by
which it is otherwise bound or, to the Issuer's knowledge, any statute, rule or
regulation (federal, state, local or foreign) to which it is subject.

          4.5  SEC Documents. The Issuer has provided the Annual Report, the
               -------------
Quarterly Report and the Proxy Statement to the Purchaser. As of the date
hereof, the Annual Report, the Quarterly Report and the Proxy Statement do not
contain any untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary in order to make the statements
therein, in light of the circumstances under which they were made, not
misleading. The financial statements of the Issuer included in the Annual Report
have been prepared in accordance with generally accepted accounting principles
applied on a consistent basis during the periods involved (except as may be
indicated in the notes thereto) and fairly present the financial position of the
Issuer as of the dates thereof and the results of its operations and cash flows
for the periods then ended. The Issuer has included in the Annual Report all
material agreements, contracts and other documents that it reasonably believes
are required to be filed as exhibits to the Annual Report.

          4.6  Litigation. There is no litigation or other legal, administrative
               ----------
or governmental proceeding pending or, to the knowledge of the Issuer,
threatened against or relating to the Issuer or its properties or business, that
if determined adversely to the Issuer may reasonably be expected to have a
material adverse effect on the present or future operations or financial
condition of the Issuer.

          4.7  No Material Adverse Change. Since the date of the Quarterly
               --------------------------
Report, there has not been any material adverse change in the business,
operations, properties, prospects,

<PAGE>

assets, or condition of the Issuer, and no event has occurred or circumstance
exits that may result in such a material adverse change.

          4.8  Environmental Matters.
               ---------------------

               (a)  Except as would not be reasonably likely to have a material
adverse effect change in the business, operations, properties, prospects,
assets, or condition of the Issuer: (i) to Issuer's knowledge, Issuer has
complied with all applicable Environmental Laws (as defined in Section 4.8(b));
(ii) to Issuer's knowledge, Issuer is not subject to liability for any Hazardous
Substance disposal or contamination on any third party property; (iii) to
Issuer's knowledge, Issuer has not been associated with any release or threat of
release of any Hazardous Substance; (v) Issuer has not received any notice,
demand, letter, claim or request for information alleging that Issuer may be in
violation of or liable under any Environmental Law; (vi) Issuer is not subject
to any orders, decrees, injunctions or other arrangements with any Governmental
Entity or is subject to any indemnity or other agreement with any third party
relating to liability under any Environmental Law or relating to Hazardous
Substances; and (vii) there are no circumstances or conditions involving Issuer
that could reasonably be expected to result in any claims, liability,
investigations, costs or restrictions on the ownership, use or transfer of any
property of Issuer pursuant to any Environmental Law.

               (b)  For purposes of this Agreement, the term "Environmental Law"
                                                              ------------------
means any federal, state, local or foreign law, regulation, order, decree,
permit, authorization, opinion, common law or agency requirement relating to:
(A) the protection, investigation or restoration of the environment, health and
safety, or natural resources, (B) the handling, use, presence, disposal, release
or threatened release of any Hazardous Substance or (C) noise, odor, wetlands,
pollution, contamination or any injury or threat of injury to persons or
property.

               (c)  For purposes of this Agreement, the term "Hazardous
                                                              ---------
Substance" means any substance that is: (A) listed, classified or regulated
---------
pursuant to any Environmental Law; (B) any petroleum product or by-product,
asbestos-containing material, lead-containing paint or plumbing, polychlorinated
biphenyls, radioactive materials or radon; or (C) any other substance which is
the subject of regulatory action by any governmental entity pursuant to any
Environmental Law.

          4.9  Most Favorable Terms. (a)During the period beginning
               --------------------
November 5, 1999 and ending on the date of this Agreement, the Issuer has not
sold any shares of its common stock for a price of less than $0.675 per share or
on terms and conditions otherwise more favorable to any purchaser of Issuer's
common stock than the terms and conditions set forth in this Agreement; provided
                                                                        --------
that the representation of Issuer in this Section 4.9(a) shall not apply to the
terms and conditions of the agreement between the Issuer and Juneau Exploration,
Inc. (the "Juneau Agreement"). All shares of common stock sold by Issuer since
November 5, 1999, the purchasers thereof, the number of shares purchased and the
dollar amount paid by each purchaser are set forth on Schedule 4.9(a).
                                                      ----------------

               (b)  In the event of any sale of common stock by Issuer that
would constitute a breach of Section 4.9(a), (i) such sale shall be considered
an issuance of additional shares of common stock under Section 4.C of the
Warrant and the number of Warrant Shares for which the Warrant is exercisable
shall be adjusted as provided therein, and (ii) the number of Shares Purchaser
is purchasing under this Agreement shall be adjusted as if Section 4.C of the
Warrant

<PAGE>

applied to such Shares, and without additional consideration on the part of
Purchaser, Issuer shall deliver such additional Shares to Purchaser.

          4.10 Juneau Agreement. Issuer has delivered a true and correct copy of
               ----------------
the Juneau Agreement to Purchaser, and since the date received by Purchaser the
Juneau Agreement has not been amended or modified in any respect orally or in
writing, is in full force and effect and has not been terminated.

          5.   Restrictions on Transfer.
               ------------------------

               5.1  Resale Restrictions. The Purchaser understands that the
                    -------------------
offer and sale of the Securities to the Purchaser has not been registered under
the Securities Act or under any State Laws. The Purchaser agrees not to offer,
sell or otherwise transfer the Securities, or any interest in the Securities,
unless (i) the offer and sale is registered under the Securities Act, (ii) the
Securities may be sold in accordance with the applicable requirements and
limitations of Rule 144 under the Securities Act and any applicable State Laws
and, if the Issuer reasonably requests, the Purchaser delivers to the Issuer an
opinion of counsel to such effect, or (iii) the Purchaser delivers to the Issuer
an opinion of counsel reasonably satisfactory to the Issuer that the offer and
sale is otherwise exempt from Securities Act registration. Notwithstanding the
foregoing subsections (ii) and (iii), no opinion shall be required for transfers
by Purchaser to Purchaser's affiliates.

               5.2  Restrictive Legend.  The Purchaser understands and agrees
                    ------------------
that a legend in substantially the following form will be placed on the
 certificates or other documents representing the Securities:

        "THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
        UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR
        UNDER ANY STATE SECURITIES LAWS AND MAY NOT BE OFFERED, SOLD OR
        OTHERWISE TRANSFERRED UNLESS (i) THE OFFER AND SALE IS REGISTERED UNDER
        THE SECURITIES ACT, OR (ii) THE OFFER AND SALE IS EXEMPT FROM SECURITIES
        ACT REGISTRATION AND THE TERMS OF SECTION 5.2 OF THE SECURITIES PURCHASE
        AGREEMENT PURSUANT TO WHICH THE SECURITIES WERE ORIGINALLY PURCHASED
        HAVE BEEN COMPLIED WITH. (A COPY OF THE SECURITIES PURCHASE AGREEMENT IS
        ON FILE AT THE CORPORATE OFFICE OF THE ISSUER.)"

                  5.3 Illiquid Investment. The Purchaser acknowledges that it
                      -------------------
must bear the economic risk of its investment in the Securities for an
indefinite period of time, until such time as the Securities are registered or
as an exemption from registration is available. The Purchaser acknowledges that
the soonest that the Rule 144 exemption from registration could become available
would be after the Purchaser has paid for and held the Securities for one year.

          6.   Right To Additional Securities
               ------------------------------

               6.1  First Refusal Rights. Subject to the terms and conditions
                    --------------------
of this Article 6, the Issuer hereby grants to the Purchaser a right of first
refusal to purchase its Pro Rata Share (as defined below) of any issue of New
Securities (as defined below) that the Issuer (or any subsidiary whose capital
stock will not be wholly owned, directly or indirectly, by the Issuer upon

<PAGE>

completion of any such issuance) may from time to time after the date of this
Agreement propose to issue.

               6.2  New Securities. "New Securities" shall mean any capital
                    --------------
stock, any rights, options or warrants to purchase or subscribe for capital
stock, and any securities or other instruments of any type whatsoever that are,
or may become, convertible into or exchangeable for capital stock, which are
issued for cash; provided, however, that "New Securities" shall not include: (i)
up to 5,000,000 shares of the Issuer's Common Stock (or related options or
rights) issued to the Issuer's employees, directors and consultants pursuant to
a plan adopted by the Board of Directors; (ii) shares of the Issuer's capital
stock issued in connection with any warrant, option or right, stock split or
stock dividend by the Issuer outstanding on the date hereof; and (iii) shares
issued to Glenn Dillon, the Issuer's controller, in an amount not to exceed
1,250 per month.

               6.3  Notice and Allocation Periods. If the Issuer or, when
                    -----------------------------
applicable, its subsidiary, proposes to undertake a bona fide issuance of New
Securities, then it shall give the Purchaser written notice of its intention,
describing the type of New Securities, the price, the number of shares to be
offered, and the general terms upon which such securities are proposed to be
offered. The Purchaser shall be given at least 20 days' prior written notice
within which to agree to purchase all or any part of its Pro Rata Share (as
hereinafter defined) of such issuance of New Securities for the price and upon
the general terms specified in said notice by giving written notice to the
issuer within such period and stating therein the quantity of New Securities to
be purchased by it. "Pro Rata Share" shall mean that portion of the number of
shares of New Securities proposed to be issued that equals the proportion that
(a) the number of shares of common stock held by the Purchaser immediately prior
to the proposed issuance, plus the number of shares of common stock that would
then be issuable to the Purchaser assuming that the Warrant had been fully
exercised, bears to (b) the total number of shares of common stock issued and
outstanding immediately prior to the proposed issuance.

               6.4  Right of Issuer to Sell New Securities. If the Purchaser
                    --------------------------------------
fails to exercise in full its rights of first refusal within the applicable
period set forth above, then the Issuer or, when applicable, its subsidiary
shall have 120 days thereafter to sell the New Securities respecting that the
rights set forth herein were not exercised at a price and upon general terms no
more favorable to the purchaser thereof than specified in the notice to the
Purchaser. If such New Securities have not been sold within such 120-day period,
then the Issuer or, when applicable, its subsidiary shall not thereafter issue
or sell any New Securities without first offering them to the Purchaser in the
manner provided above.

               6.5  Right to Additional Securities. If the Issuer sells or
                    ------------------------------
grants shares of its common stock or other securities convertible into its
common stock at a price per share of common stock less than $0.675 during the
45-day period commencing on the date of this Agreement, then the Issuer shall
promptly issue to Purchaser a number of additional shares of common stock equal
to the aggregate Purchase Price divided by the per share price at which the
subsequently issued securities (on a per share basis) were issued, less
3,703,704.

          7.   Registration Procedures.
               -----------------------

          7.1  Initial Filing.  Within 90 days after the issuance of the Shares,
               --------------
 the Issuer shall prepare and file or cause to be filed with the SEC a
 registration statement (the "Initial


<PAGE>

Registration Statement") with respect to the Shares. The Issuer shall thereafter
use diligence in attempting to cause the Initial Registration Statement to be
declared effective by the SEC and shall thereafter use diligence to maintain the
effectiveness of the Initial Registration Statement until the earlier to occur
of (i) the date which is one year from the effective date of the Initial
Registration Statement, (ii) the date on which all of the Shares have been sold
by the Purchaser or (iii) the date on which the Shares can be resold in full
over a three-month period pursuant to SEC Rule 144.

          7.2  Demand Registration Rights. (a) If at any time the Initial
               --------------------------
Registration Statement is no longer effective, Purchaser shall be entitled to
make a request for registration under the Securities Act of Shares or Warrant
Shares (together, "Registerable Securities") in an aggregate amount of at least
1,111,111 shares (a "Demand Registration"). Within 120 days of the receipt of a
written request for a Demand Registration, the Issuer shall file with the SEC
and use its best efforts to cause to become effective under the Securities Act a
registration statement with respect to such Registerable Securities (a "Demand
Registration Statement"). Any such request will specify the number of
Registerable Securities proposed to be sold and will also specify the intended
method of disposition thereof. The Issuer shall be required to register
Registerable Securities pursuant to this Section 7.2 on a maximum of two
separate occasions; provided, the Issuer shall not be required to register
Registerable Securities pursuant to this Section 7.2 more than once in any
twelve month period.

               Subject to Section 7.2(b) hereof, no other securities of the
Issuer except securities held by Purchaser, any persons with "demand"
registration rights pursuant to a contractual commitment of the Issuer ("Demand
Right Holder"), and any Person entitled to exercise "piggy back" registration
rights pursuant to contractual commitments of the Issuer shall be included in a
Demand Registration.

               (b)  In a registration pursuant to Section 7.2(a) hereof
involving an underwritten offering, if the managing underwriter or underwriters
of such underwritten offering have informed, in writing, the Issuer and the
Purchaser that in such underwriter's or underwriters' opinion the total number
of securities which the Purchaser and any other person desiring to participate
in such registration intend to include in such offering is such as to adversely
affect the success of such offering, including the price at which such
securities can be sold, then the Issuer will be required to include in such
registration only the amount of securities which it is so advised should be
included in such registration. In such event, securities shall be registered in
such registration in the following order of priority: (i) first, the
                                                          -----
Registerable Securities which have been requested to be included in such
registration by the Purchaser and person(s) exercising demand registration
rights (whether pursuant to this Agreement or otherwise) (pro rata based on the
amount of securities sought to be registered by such Persons), (ii) second,
provided that no securities sought to be included by the Purchasers and the
Demand Right Holders have been excluded from such registration, the securities
of other persons entitled to exercise "piggy-back" registration rights pursuant
to contractual commitments of the Issuer (pro rata based on the amount of
securities sought to be registered by such Persons) and (iii) third, securities
the Issuer proposes to register.

               (c)  A Demand Registration Statement will not be deemed to have
been effected as a Demand Registration unless it has been declared effective by
the SEC and the Issuer has complied in a timely manner and in all material
respects with all of its obligations under this Agreement with respect thereto;
provided, however, that if, after such Demand
--------  -------

<PAGE>

Registration Statement has become effective, the offering of Registerable
Securities pursuant to such Registration Statement is or becomes the subject of
any stop order, injunction or other order or requirement of the SEC or any other
governmental or administrative agency or court that prevents, restrains or
otherwise limits the sale of Registerable Securities pursuant to such Demand
Registration Statement for any reason not attributable to Purchaser and such
Demand Registration Statement has not become effective within a reasonable time
period thereafter (not to exceed 60 days), such Demand Registration Statement
will be deemed not to have been effected. If (i) a registration requested
pursuant to this Section 7.2 is deemed not to have been effected or (ii) a
Demand Registration does not remain effective under the Securities Act until at
least the earlier of (A) an aggregate of 90 days after the effective date
thereof or (B) the consummation of the distribution by the Purchaser of 80% of
Purchaser's Registerable Securities covered thereby, then the Company shall
continue to be obligated to effect a Demand Registration pursuant to this
Section 7.2. For purposes of calculating the 90-day period referred to in the
preceding sentence, any period of time during which such Demand Registration
Statement was not in effect shall be excluded.

     7.3  Piggy-Back Registration Rights. (a) If at any time the Initial
          ------------------------------
Registration Statement is no longer effective the Issuer proposes to file a
registration statement under the Securities Act with respect to an offering by
the Issuer for its own account or for the account of any of its securityholders
of any class of its Common Stock in a firmly underwritten public equity offering
(other than (i) a registration statement on Form S-4 or S-8 (or any substitute
form that may be adopted by the SEC) or (ii) a registration statement filed in
connection with an exchange offer or offering of securities solely to the
Issuer's existing securityholders), then the Issuer shall give written notice of
such proposed filing to the Purchaser as soon as practicable (but in no event
fewer than 30 days before the anticipated filing date), and such notice shall
offer Purchaser the opportunity to register such number of Registerable
Securities as Purchaser may request in writing within 15 days after receipt of
such written notice from the Issuer (which request shall specify the shares
intended to be disposed of by Purchaser) (a "Piggy-Back Registration"). The
                                             -----------------------
Issuer shall use its best efforts to keep such Piggy-Back Registration
continuously effective under the Securities Act until at least the earlier of
(A) the 90th day after the effective date thereof or (B) the consummation of the
distribution by the holders of all of the securities covered thereby. The Issuer
shall use its best efforts to cause the managing underwriter or underwriters, if
any, of such proposed offering to permit the Registerable Securities requested
by Purchaser to be included in a Piggy-Back Registration to be included on the
same terms and conditions as any similar securities of the Issuer or any other
securityholder included therein and to permit the sale or other disposition of
such Registerable Securities in accordance with the intended method of
distribution thereof. Purchaser shall have the right to withdraw its request for
inclusion of its Registerable Securities in any Registration Statement pursuant
to this Section 7.3 by giving written notice to the Issuer of its request to
withdraw. The Issuer may withdraw a Piggy-Back Registration at any time prior to
the time it becomes effective or the Issuer may elect to delay the registration;
provided, however, that the Issuer shall give prompt written notice thereof to
--------  -------
Purchaser.

          No registration effected under this Section 7.3, and no failure to
effect a registration under this Section 7.3, shall relieve the Issuer of its
obligation to effect a registration upon the request of Purchaser pursuant to
Section 7.2 hereof, and no failure to effect a registration under this Section
7.3 and to complete the sale of securities registered thereunder in connection
therewith shall relieve the Issuer of any other obligation under this Agreement.

<PAGE>

          (b)  In a registration pursuant to Section 7.3 hereof involving an
underwritten offering, if the managing underwriter or underwriters of such
underwritten offering have informed, in writing, the Issuer and the
securityholders requesting inclusion in such offering that in such underwriter's
or underwriters' opinion the total number of securities which the Issuer, the
Purchaser and any other persons desiring to participate in such registration
intend to include in such offering is such as to adversely affect the success of
such offering, including the price at which such securities can be sold, then
the Issuer will be required to include in such registration only the amount of
securities which it is so advised should be included in such registration. In
such event: (x) in cases initially involving the registration for sale of
securities for the Issuer's own account, securities shall be registered in such
offering in the following order of priority: (i) first, the securities which the
                                                 -----
Issuer proposes to register and (ii) second, the securities which have been
                                     ------
requested to be included in such registration by persons entitled to exercise
"piggy-back" registration rights pursuant to contractual commitments of the
Issuer (pro rata based on the amount of securities sought to be registered by
such persons); and (y) in cases not initially involving the registration for
sale of securities for the Issuer's own account, securities shall be registered
in such offering in the following order of priority: (i) first, the securities
                                                         -----
of any Demand Right Holder whose exercise of a demand registration right is the
basis for the registration, (ii) second, securities of other persons entitled to
                                 ------
exercise "piggy-back" registration rights pursuant to contractual commitments
(pro rata based on the amount of securities sought to be registered by such
Persons) and (iii) third, the securities which the Issuer proposes to register.
                   -----

     7.4  Following effectiveness of any registration statement filed by Issuer
pursuant ot Sections 7.1, 7.2 or 7.3 of this Agreement ("a Registration
Statement"), the Issuer shall furnish to the Purchaser a prospectus as well as
such other documents as the Purchaser may reasonably request.

     7.5  Without the written consent of the Purchaser, the Issuer shall not
grant to any person the right to request the Issuer to register any securities
of the Issuer under the Securities Act unless the rights so granted are subject
to the prior rights of the Purchaser set forth herein, and are not otherwise in
conflict or inconsistent with the provisions of this Agreement; provided, that
                                                                --------
Issuer may grant to the Southern Ute tribe rights that are pari passu with the
rights of Purchaser set forth herein, in connection with the sale of Issuer's
common stock to the Southern Ute tribe prior to March 1, 2000 at a per share
price of not less than $0.675 and one or more warrants to purchase shares of
Issuer's common stock not in excess of ten percent of the common stock sold to
the Southern Ute tribe in such transaction.

     7.6  The Issuer shall use diligent efforts to (i) register or otherwise
qualify the common stock covered by the Registration Statement for sale under
the securities laws of such jurisdictions as the Purchaser may reasonably
request, (ii) prepare and file in those jurisdictions such amendments (including
post-effective amendments) and supplements as may be required, (iii) take such
other actions as may be necessary to maintain such registrations and/or
qualifications in effect at all times while the Registration Statement is
likewise maintained effective and (iv) take all other actions reasonably
necessary or advisable to qualify the Shares for sale in such jurisdictions;
provided, however, that the Issuer shall not be required in connection therewith
or as a condition thereto to (I) qualify to do business in any jurisdiction
where it would not otherwise be required to qualify but for this Section 7.6,
(II) subject itself to general taxation in any such jurisdiction, (III) file a
general consent to service of process in any such jurisdiction, (IV) provide any
undertakings that cause more than nominal expense or burden

<PAGE>

to the Issuer or (V) make any change in its certificate of incorporation or
bylaws, which in each case the Board determines to be contrary to the best
interests of the Issuer and its stockholders.

     7.7  The Issuer shall, following effectiveness of the Registration
Statement, as promptly as practicable after becoming aware of any such event,
notify the Purchaser of the happening of any event of which the Issuer has
knowledge, as a result of which the prospectus included in the Registration
Statement, as then in effect, includes an untrue statement of a material fact or
omits to state a material fact required to be stated therein or necessary to
make the statements therein, in light of the circumstances under which they were
made, not misleading, and use its best efforts promptly to prepare a supplement
or amendment to the Registration Statement to correct such untrue statement or
omission, and deliver a number of copies of such supplement or amendment to the
Purchaser or as the Purchaser may reasonably request. The Issuer may voluntarily
suspend once the effectiveness of a Registration Statement for a limited time,
which in no event shall be longer than 90 days, if the Issuer has been advised
by legal counsel that the offering of common stock pursuant to the Registration
Statement would adversely affect, or would be improper in view of (or improper
without disclosure in a prospectus), a proposed financing, a reorganization,
recapitalization, merger, consolidation, or similar transaction involving the
Issuer or its subsidiaries, in which event the one year period referred to in
clause (i) of Section 7.6 shall be extended for an additional period of time
beyond such one year period equal to the number of days the effectiveness
thereof has been suspended pursuant to this sentence.

     7.8  Following effectiveness of a Registration Statement, the Issuer, as
promptly as practicable after becoming aware of any such event, will notify the
Purchaser of the issuance by the SEC of any stop order or other suspension of
effectiveness of the Registration Statement at the earliest possible time.

     7.9  Following effectiveness of a Registration Statement, the Issuer will
use diligence either to (i) cause all the common stock covered by the
Registration Statement to be listed on each national securities exchange on
which similar securities issued by the Issuer are then listed, if any, if the
listing of such common stock is then permitted under the rules of such exchange,
or (ii) secure the quotation of all the common stock covered by the Registration
Statement on The Nasdaq SmallCap Market, if the listing of such common stock is
then permitted under the rules of such The Nasdaq SmallCap Market, or (iii) if,
despite the Issuer's best efforts to satisfy the preceding clause (i) or (ii),
the Issuer is unsuccessful in satisfying the preceding clause (i) or (ii) and
without limiting the generality of the foregoing, to use its best efforts to
arrange for at least two market makers to register with the National Association
of Securities Dealers, Inc. as such with respect to such common stock.

     7.10 It shall be a condition precedent to the obligations of the Issuer to
take any action pursuant to this Section 7 that the Purchaser shall furnish to
the Issuer such information regarding itself as the Issuer may reasonably
request to effect the registration of the common stock and shall execute such
documents in connection with such registration as the Issuer may reasonably
request.

     7.11 The Purchaser agrees to cooperate with the Issuer in any manner
reasonably requested by the Issuer in connection with the preparation and filing
of a Registration Statement hereunder.

<PAGE>

     7.12 The Purchaser agrees that, upon receipt of any notice from the Issuer
of the happening of any event of the kind described in Section 7.7 or 7.8, the
Purchaser will immediately discontinue disposition of Shares pursuant to an
effective Registration Statement until the Purchaser's receipt of notice from
the Issuer that sales may resume and copies of the supplemented or amended
prospectus and, if so directed by the Issuer, shall deliver to the Issuer (at
the expense of the Issuer) or destroy (and deliver to the Issuer a certificate
of destruction) all copies in the Purchaser's possession of the prospectus
covering such Common Stock current at the time of receipt of such notice.

     7.13 All expenses, other than (i) underwriting discounts and commissions,
(ii) other fees and expenses of investment bankers and (iii) brokerage
commissions, incurred in connection with registrations, filings or
qualifications pursuant to this Section 7, including, without limitation, all
registration, listing and qualification fees, printing and accounting fees and
the fees and disbursements of counsel to the Issuer, shall be borne by the
Issuer.

     7.14 To the extent permitted by law, the Issuer will indemnify and hold
harmless the Purchaser, its directors and officers, each person, if any, who is
under common control with the Purchaser within the meaning of the Securities Act
or the Securities Exchange Act of 1934, as amended (the "Exchange Act"), any
underwriter (as defined in the Securities Act) for the Purchaser, the officers
and directors of such underwriter and each person, if any, who controls any such
underwriter within the meaning of the Securities Act or the Exchange Act (each,
an "Indemnified Person"), against any losses, claims, damages, expenses or
liabilities (joint or several) (collectively, "Claims") to which any of them may
become subject under the Securities Act, the Exchange Act or otherwise, insofar
as such Claims (or actions or proceedings, whether commenced or threatened, in
respect thereof) arise out of or are based upon any of the following statements,
omissions or violations in a Registration Statement, or any post effective
amendment thereof, or any prospectus included therein: (i) any untrue statement
or alleged untrue statement of a material fact contained in a Registration
Statement or any post effective amendment thereof or the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, (ii) any untrue
statement or alleged untrue statement of a material fact contained in any
preliminary prospectus if used prior to the effective date of a Registration
Statement, or contained in the final prospectus (as amended or supplemented, if
the Issuer files any amendment thereof or supplement thereto with the SEC) or
the omission or alleged omission to state therein any material fact necessary to
make the statements made therein, in light of the circumstances under which the
statements therein were made, not misleading or (iii) any violation or alleged
violation by the Issuer of the Securities Act, any state securities law or any
rule or regulation under the Securities Act, the Exchange Act or any state
securities law (the matters in the foregoing clauses (i) through (iii) are
hereinafter collectively referred to as the "Violations"). Subject to the
restrictions set forth in Section 7.15 with respect to the number of legal
counsel, the Issuer shall reimburse the Purchaser and each such underwriter or
controlling person, promptly as such expenses are incurred and are due and
payable, for any reasonable legal fees or other reasonable expenses incurred by
them in connection with investigating or defending any such Claim.
Notwithstanding anything to the contrary contained herein, the indemnity
contained in this Section 7.13 (I) shall not apply to a Claim arising out of or
based upon a Violation which occurs in reliance upon and in conformity with
information furnished in writing to the Issuer by any Indemnified Person or
underwriter for such Indemnified Person expressly for use in connection with the
preparation of a Registration Statement or any such amendment thereof or
supplement thereto; (II) with respect to any preliminary prospectus shall not
inure to the benefit of any person from whom the person

<PAGE>

asserting any Claim purchased the Shares that are the subject thereof (or to the
benefit of any person controlling such person) if the untrue statement or
omission of material fact contained in the preliminary prospectus was corrected
in the prospectus, as then amended or supplemented, if such final prospectus was
timely made available by the Issuer; and (III) shall not apply to amounts paid
in settlement of any Claim if such settlement is effected without the prior
written consent of the Issuer, which consent shall not be unreasonably withheld.
Such indemnity shall remain in full force and effect regardless of any
investigation made by or on behalf of the Indemnified Person and shall survive
the transfer of the Shares by the Purchaser.

     7.15 The Purchaser agrees to indemnify and hold harmless, to the same
extent and in the same manner set forth in Section 7.14, the Issuer, each of its
directors, each of its officers who signs a Registration Statement, each person,
if any, who controls the Issuer within the meaning of the Securities Act or the
Exchange Act, any underwriter and any other stockholder selling securities
pursuant to a Registration Statement or any of its directors or officers or any
person who controls such stockholder or underwriter within the meaning of the
Securities Act or the Exchange Act (each such person and each Indemnified
Person, an "Indemnified Party"), against any Claim to which any of them may
become subject, under the Securities Act, the Exchange Act or otherwise, insofar
as such Claim arises out of or is based upon any Violation by the Purchaser, in
each case to the extent (and only to the extent) that such Violation occurs in
reliance upon and in conformity with written information furnished to the Issuer
by the Purchaser expressly for use in connection with such Registration
Statement or such prospectus; and the Purchaser will reimburse any reasonable
legal or other expenses reasonably incurred by any Indemnified Party in
connection with investigating or defending any such Claim; provided, however,
that the indemnity contained in this Section 7.15 shall not apply to amounts
paid in settlement of any Claim if such settlement is effected without the prior
written consent of the Purchaser, which consent shall not be unreasonably
withheld; provided, further, that the Purchaser shall be liable under this
Section 7.15 for only that amount of a Claim as does not exceed the net proceeds
to the Purchaser as a result of the sale of Shares pursuant to any such
Registration Statement or such prospectus. Such indemnity shall remain in full
force and effect regardless of any investigation made by or on behalf of such
Indemnified Party and shall survive the transfer of the Shares (or underlying
securities) by the Purchaser. Notwithstanding anything to the contrary contained
herein the indemnity contained in this Section 7.15 with respect to any
preliminary prospectus shall not inure to the benefit of any Indemnified Party
if the untrue statement or omission of material fact contained in the
preliminary prospectus was corrected on a timely basis in the prospectus, as
then amended or supplemented.

     7.16 Promptly after receipt by an Indemnified Person or Indemnified Party
under Section 7.14 or 7.15 of notice of the commencement of any action
(including any governmental action), such Indemnified Person or Indemnified
Party shall, if a Claim in respect thereof is made against any indemnifying
party under this Section 7, deliver to the indemnifying party a written notice
of the commencement thereof, and the indemnifying party shall have the right to
participate in, and, to the extent the indemnifying party so desires, jointly
with any other indemnifying party similarly noticed, assume control of the
defense thereof with counsel mutually satisfactory to the indemnifying parties;
provided, however, that an Indemnified Person or Indemnified Party shall have
the right to retain its own counsel, with the fees and expenses to be paid by
the indemnifying party, if, in the reasonable opinion of counsel retained by the
indemnifying party, the representation by such counsel of the Indemnified Person
or Indemnified Party and the indemnifying party would be inappropriate due to
actual or potential differing interests between such Indemnified Person or
Indemnified Party and any other party represented

<PAGE>

by such counsel in such proceeding. Except as provided in the preceding
sentence, the Issuer shall pay for only one separate legal counsel for the
Indemnified Persons. The failure to deliver written notice to the indemnifying
party within a reasonable time of the commencement of any such action shall not
relieve such indemnifying party of any liability to the Indemnified Person or
Indemnified Party under this Section 7, except to the extent that the
indemnifying party is prejudiced in its ability to defend such action. The
indemnity required by this Section 7 shall be made by periodic payments of the
amount thereof during the course of the investigation or defense, as such
expense, loss, damage or liability is incurred and is due and payable.

     8.   Transfer Agent Instructions. The Issuer will instruct its transfer
          ---------------------------
agent to, concurrently with the delivery by the Purchaser of the Purchase Price,
issue one or more certificates representing the Shares purchased, bearing the
restrictive legend specified in Section 5.2 of this Agreement, registered in the
name of the Purchaser or its nominee and in such denominations as shall be
specified by the Purchaser. The Issuer warrants that no instruction other than
to issue the shares and stop transfer instructions to give effect to Section 5.1
and 5.2 hereof will be given by the Issuer to the transfer agent and that the
Shares shall otherwise be freely transferable on the books and records of the
Issuer as and to the extent provided in this Agreement. Nothing in this Section
shall affect in any way the Purchaser's obligations and agreement to comply with
all applicable federal and state securities laws upon resale of the Shares. If
the Purchaser provides the Issuer with an opinion of counsel reasonably
satisfactory in form, scope and substance to the Issuer that registration of a
resale by the Purchaser of any of the Shares in accordance with Section 5.1 is
not required under the Securities Act or applicable state securities laws, the
Issuer shall permit the transfer agent to issue one or more share certificates
in such name and in such denominations as specified by the Purchaser.

     9.   Board of Directors. The Issuer's board shall consist of not more than
          ------------------
seven members. Issuer shall not amend or cause to be amended its charter in
effect on the date hereof as to the number of members of Issuer's Board without
the prior written consent of Purchaser, so long as Purchaser holds at least five
percent (5%) of the Issuer's outstanding common stock. If at any time Purchaser
has not appointed or nominated for election at least one of the members of the
Issuer's Board and Purchaser then holds at least five percent (5%) of the
Issuer's outstanding common stock, then Purchaser shall be entitled to appoint
one observer to the Issuer's Board (the "Observer"). Such Observer shall have
the right to attend, and receive all materials distributed for or at, all
meetings (telephonic and otherwise) of the Board (including committees thereof)
and shall be entitled to the same rights and privileges as directors of the
Issuer, except that such Observer shall not be entitled to vote on matters
presented to or discussed by the Board. The Observer will receive no
compensation from the Issuer for his services as observer, but shall be entitled
to be reimbursed by the Issuer for all reasonable costs and expenses incurred in
connection with his participation in meetings or other activities of the Board.

     10.  Reliance. Each of the Purchaser and the Issuer understand and agree
          --------
that the other party and its respective officers, directors, employees and
agents may, and will, rely on the accuracy of the other party's respective
representations and warranties in this agreement to establish compliance with
applicable securities laws. Each of the Purchaser and the Issuer agree to
indemnify and hold harmless all such parties against all losses, claims, costs,
expenses and damages or liabilities which they may suffer or incur caused or
arising from their reliance on such representations and warranties.

<PAGE>

     11.  Covenant to Amend Existing Bylaws. Within 14 days of the date hereof,
          ---------------------------------
the Issuer agrees to amend and restate its existing Bylaws substantially in the
form attached hereto as Exhibit B and in a form that is reasonably satisfactory
to TCW.

     12.  Miscellaneous.
          -------------

          12.1  Survival. The representations and warranties made in this
                --------
Agreement shall survive the closing of the transactions contemplated by this
Agreement.

          12.2  Assignment. This Agreement is not transferable or assignable,
                ----------
except that the rights of Purchaser and the obligations of Issuer set forth in
Section 5, 6 and 7 hereof shall be transferable to an affiliate of Purchaser
(including, without limitation, any affiliate of, or investment fund or account
managed by any affiliated of, The TCW Group, Inc. and any beneficiary or
beneficial interest holder of any such fund or account) and any transferee of
Purchaser's Securities who receives at least 30% of the Securities to be issued
hereby.

          12.3  Execution and Delivery of Agreement. The Issuer shall be
                -----------------------------------
entitled to rely on delivery by facsimile transmission of an executed copy of
this agreement, and acceptance by the Issuer of such facsimile copy shall create
a valid and binding agreement between the Purchaser and the Issuer.

          12.4  Titles. The titles of the sections and subsections of this
                ------
agreement are for the convenience of reference only and are not to be considered
in construing this agreement.

          12.5  Severability. The invalidity or unenforceability of any
                ------------
particular provision of this agreement shall not affect or limit the validity or
enforceability of the remaining provisions of this agreement.

          12.6  Entire Agreement. This agreement constitutes the entire
                ----------------
agreement and understanding between the parties with respect to the subject
matters herein and supersedes and replaces any prior agreements and
understandings, whether oral or written, between them with respect to such
matters.

          12.7  Waiver and Amendment. Except as otherwise provided herein, the
                --------------------
provisions of this agreement may be waived, altered, amended or repealed, in
whole or in part, only upon the mutual written agreement of the Purchaser and
the Issuer.

          12.8  Counterparts. This agreement may be executed in any number of
                ------------
counterparts, each of which shall be an original, but all of which together
shall constitute one and the same instrument.

          12.9  Governing Law. This agreement is governed by and shall be
                -------------
construed in accordance with the laws of the State of Nevada.

          12.10 Expense Reimbursement. Issuer shall pay $40,000 pursuant to the
                ---------------------
instruction of Purchaser as reimbursement for Purchaser's legal fees and costs
in connection with the purchase of the Securities.

<PAGE>

     IN WITNESS WHEREOF, the parties hereto have duly executed this agreement as
of the date first above mentioned.

THE "ISSUER"                               THE "PURCHASER"

CONTANGO OIL & GAS 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

     /s/ Kenneth R. Peak                        /s/ Arthur R. Carlson
By:________________________________        By:__________________________________
     Kenneth R. Peak                            Arthur R. Carlson
     President and Chief Executive              Managing Director
      Officer
                                                /s/ Thomas F. Mehlberg
                                           By:__________________________________
                                                Thomas F. Mehlberg
                                                Managing Director

<PAGE>

                                    EXHIBIT A
                                 FORM OF WARRANT

                                     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 and from time to 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 traded over the
5-trading day period immediately prior to such date or, if the Common Stock is
not then traded on a securities exchange or national market system, the average
of the bid and asked prices on the over-the-counter market on which the Common
Stock is then traded over the 5-trading day period immediately prior to such
date.

<PAGE>

               "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 or, if the Common Stock is
not then traded on a securities exchange or national market system, the average
of the bid and asked prices on the over-the-counter market on which the Common
Stock is then traded 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) up to 5,000,000 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, (iv) any shares of Common Stock issued
pursuant to the Company's agreement with Juneau Exploration dated August 1,
1999, (v) any shares of Common Stock sold to the Southern Ute tribe prior to
March 1, 2000 at a per share price of not less than $0.675 and one or more
warrants to purchase shares of Common Stock not in excess of ten percent of the
Common Stock sold to the Southern Ute tribe in such transaction, and (vi) shares
of Common Stock in a number not to exceed 1,250 per month issued to Glenn
Dillon.

               "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 States of Texas or California.

               "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

<PAGE>

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 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

<PAGE>

(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.

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

<PAGE>

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.

          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

<PAGE>

          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

                    (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 greater of (i) the Current Market Price per share of Common
Stock or (ii) the Current Warrant 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 greater of (A) 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
Warrant Price per share of Common Stock, and (ii) the denominator of which shall
be the consideration per share received by the Company for such Additional
Shares of Common Stock or (B) 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 greater of the Current Warrant Price of
the Current Market Price per share of Common Stock. For purposes of this
Subsection, the date as of which the Current Market Price and the Current
Warrant Price per share of Common Stock shall be

<PAGE>

computed shall be the earlier of (i) the date on which the Company shall enter
into a firm contract for the issuance of such Additional Shares of Common Stock,
or (ii) 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 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 greater of (i) the Current Market Price per share of Common Stock or
(ii) the Current Warrant 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 greater of those numbers determined pursuant to clauses (A) and (B) in
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 and the Current Warrant 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
greater of (i) the Current Market Price per share of Common Stock or (ii) the
Current Warrant 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
greater of those numbers determined pursuant to clauses (A) and(B) in 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 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 and the
Current Warrant Price per share of Common Stock shall be computed shall be the
earliest of (a) the date on which the

<PAGE>

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, 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:

<PAGE>

                    (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 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

<PAGE>

     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 (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.

<PAGE>

     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 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 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

<PAGE>

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.

     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

<PAGE>

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:

          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:

              Trust Company of the West
              865 S. Figueroa Street
              Los Angeles, California 90017
              Attention: Arthur R. Carlson
              Phone:       (213) 244-0053
              Fax:         (213) 244-0604

              with a copy to:

              Milbank, Tweed, Hadley & McCloy LLP
              601 S. Figueroa Street, 30th Floor
              Los Angeles, CA 90017
              Attention: David A. Lamb, Esq.
              Phone:       (213) 892-4000
              Fax:         (213) 629-5063


          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.

<PAGE>

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

<PAGE>

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: _____________________



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

                                     By:
                                        ----------------------------------------
                                        Kenneth R. Peak
                                        President and Chief Executive Officer

<PAGE>

                                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)

<PAGE>

                                 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:

                                                           No. of Stock
          Name and Address of Assignee                         Units
          ----------------------------                       ---------







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.]