<PAGE>   1

                                                                     EXHIBIT 1.1



                           QUEEN SAND RESOURCES, INC.

                   $125,000,000 12 1/2% Senior Notes due 2008

                               PURCHASE AGREEMENT


                                                                   June 30, 1998

Nesbitt Burns Securities Inc.
CIBC Oppenheimer Corp.
Societe Generale Securities Corporation
c/o      Nesbitt Burns Securities Inc.
         111 West Monroe Street
         Chicago, Illinois  60603

Ladies and Gentlemen:

         Queen Sand Resources, Inc., a Delaware corporation (the "Company"),
proposes to issue and sell to Nesbitt Burns Securities Inc., CIBC Oppenheimer
Corp. and Societe Generale Securities Corp. (each, a "Purchaser" and together,
the "Purchasers") an aggregate of $125,000,000 principal amount of its 12 1/2%
Senior Notes due 2008 (the "Notes"), subject to the terms and conditions set
forth in this Purchase Agreement (herein "this Agreement").  The Notes are to
be issued pursuant to the provisions of an indenture (the "Indenture") to be
dated as of July 1, 1998, among the Company, the Subsidiary Guarantors named
therein and Harris Trust and Savings Bank, as trustee (the "Trustee").  The
Notes will be guaranteed (the "Subsidiary Guarantees") by all existing and
future Restricted Subsidiaries (as defined in the Indenture) of the Company
(the "Subsidiary Guarantors"), as further provided in the Indenture.

         The sale of the Notes to the Purchasers will be made without
registration of the Notes under the Securities Act of 1933, as amended (the
"Securities Act"), in reliance upon the exemption from the registration
requirements of the Securities Act provided by Section 4(2) thereof.  The
Purchasers have advised the Company that the Purchasers will make offers of the
Notes purchased hereunder in accordance with Section 5 hereof on the terms set
forth in the Offering Memorandum, as amended or supplemented (as defined
below), as soon as the Purchasers deem advisable after this Agreement has been
executed and delivered, solely to (i) persons whom the Purchasers reasonably
believe to be "qualified institutional buyers" as defined in Rule 144A under
the Securities Act ("QIBs"), (ii) a limited number of institutional "accredited
investors" (as defined in rule 501(a)(1), (2), (3) or (7) under the Securities
Act) and (iii) to certain persons outside the United States in reliance on
Regulation S under the Securities Act.
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         In connection with the sale of the Notes, the Company and the
Subsidiary Guarantors have prepared a preliminary offering memorandum, dated
May 27, 1998 (the "Preliminary Offering Memorandum"), and a final offering
memorandum, dated June 30, 1998 (the "Offering Memorandum"), each setting forth
certain information concerning the Company, the Subsidiary Guarantors, the
Notes and the Subsidiary Guarantees.  The Company hereby confirms that it has
authorized the use of the Preliminary Offering Memorandum and the Offering
Memorandum in connection with the offering and resale by the Purchasers of the
Notes.  Any references herein to the Offering Memorandum shall be deemed to
include all exhibits thereto.

                 1.       Representations and Warranties of the Company and the
Subsidiary Guarantors.  Each of the Company and the Subsidiary Guarantors
represents and warrants to, and agrees with, the Purchasers that:

         (a)     The Preliminary Offering Memorandum and the Offering
Memorandum as of their respective dates did not, and the Offering Memorandum
(as the same may have been amended or supplemented) as of the Closing Date (as
defined below) will not, contain any untrue statement of a material fact or
omit to state any material fact required to be stated therein or necessary to
make the statements therein, in the light of the circumstances under which they
were made, not misleading; provided, however, that the Company makes no
representations or warranties as to the information contained in or omitted
from the Preliminary Offering Memorandum and the Offering Memorandum (and any
amendment or supplement thereof or thereto) based solely upon information
furnished in writing to the Company by or on behalf of any Purchaser relating
to such Purchaser specifically for inclusion therein.

         (b)     The documents filed by the Company under the Securities
Exchange Act of 1934, as amended (the "Exchange Act") at the time they were
filed with the Commission, complied  in all material respects with the
requirements of the Exchange Act and the rules and regulations of the
Commission thereunder and did not contain an untrue statement of a material
fact or omit to state a material fact required to be stated therein, in light
of the circumstances under which they were made, or necessary to make the
statements therein not misleading.

         (c)     Each of the Company and the Subsidiary Guarantors has been
duly organized and is validly existing as a corporation in good standing under
the laws of its jurisdiction of organization.  Each of the Company and the
Subsidiary Guarantors has full corporate power and authority to own, lease and
operate its properties and to conduct its business as described in the Offering
Memorandum.  Each of the Company and the Subsidiary Guarantors is duly
qualified and is in good standing as a foreign corporation authorized to do
business in each jurisdiction in which such qualification is required, except
where the failure to be so qualified or in good standing would not have a
material adverse effect on the business, prospects, financial condition or
results of operations of the Company and its subsidiaries taken as a whole.

         (d)     The Company's authorized capitalization is as set forth in the
Offering Memorandum, and all of the issued shares of capital stock of the
Company have been duly and





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validly authorized and issued and are fully paid and nonassessable and conform
to the description thereof contained in the Offering Memorandum.

         (e)     All the outstanding shares of capital stock of each subsidiary
of the Company have been duly and validly authorized and issued and are fully
paid and nonassessable, and, except as otherwise set forth in the Offering
Memorandum, all outstanding shares of capital stock of the subsidiaries are
owned by the Company, either directly or through wholly owned subsidiaries free
and clear of any security interests, claims, liens, encumbrances or any other
claim of any third party.

         (f)     Since the date of the most recent financial statements
included or incorporated by reference in the Offering Memorandum (exclusive of
any amendment or supplement thereof or thereto), there has been no material
adverse change, or any development which could reasonably be expected to result
in a material adverse change, in the business, prospects, financial condition
or results of operations of the Company and its subsidiaries taken as a whole,
whether or not arising from transactions in the ordinary course of business,
except as set forth in the Offering Memorandum (exclusive of any amendment or
supplement thereof or thereto); and, since the respective dates as of which
information is given in the Offering Memorandum, there has not been any change
in the capital stock (other than grants of options and issuances of common
stock pursuant to existing employee stock option plans or the exercise of
outstanding warrants to purchase shares of common stock) of the Company or any
of its subsidiaries or long-term debt of the Company or any of its
subsidiaries.

         (g)     Except as disclosed in the Offering Memorandum, there is no
action, suit, proceeding, inquiry or investigation before or by any court or
governmental agency or body, domestic or foreign, now pending, or, to the
knowledge of the Company, threatened, against or affecting the Company or any
subsidiary thereof which might reasonably be expected to result in a (i)
material adverse effect on the business, prospects, financial condition or
results of operations of the Company and its Subsidiaries taken as whole or
(ii) adversely affect in any manner the validity of this Agreement or any other
agreement entered into in connection with the issuance of and sale of the Notes
(the events referred to in clauses (i) through (ii), a "Material Adverse
Effect");

         (h)     Ernst & Young L.L.P. and KPMG Peat Marwick L.L.P., who have
certified certain financial statements included or incorporated by reference in
the Offering Memorandum, are independent public accountants within the meaning
of the Securities Act and the rules and regulations of the Securities and
Exchange Commission (the "Commission") thereunder.

         (i)     The consolidated historical financial statements (including
the related notes and supporting schedules) included or incorporated by
reference in the Offering Memorandum present fairly the consolidated financial
position of the Company and its consolidated subsidiaries as of the dates
indicated and the consolidated results of the operations and cash flows of the
Company and its consolidated subsidiaries for the periods specified.  Such
financial statements (except as disclosed in the notes thereto or otherwise
stated therein) have been prepared in conformity with generally accepted
accounting principles applied on a consistent basis throughout the periods





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involved. The selected historical consolidated financial data and the summary
historical financial information included in the Offering Memorandum present
fairly the information shown therein and have been compiled on a basis
consistent with that of the audited consolidated historical financial
statements included or incorporated by reference in the Offering Memorandum
except as otherwise specifically stated in the Offering Memorandum.  The pro
forma condensed consolidated financial statements and other pro forma
consolidated financial information included in the Offering Memorandum have
been prepared on a basis consistent with such historical consolidated financial
statements, except as described in such pro forma financial statements and
except for the pro forma adjustments specified therein, and give effect to
assumptions made on a reasonable basis and present fairly the historical and
proposed transactions described in the pro forma financial statements.

         (j)     Except as would not have a Material Adverse Effect, (i) the
Company and its subsidiaries possess all material licenses, certificates,
authorizations, permits and other authorizations issued by, (ii) have made all
declarations and filings with, the appropriate federal, state, local or foreign
regulatory agencies or bodies necessary for the ownership of their respective
properties or the conduct of their respective businesses as described in the
Offering Memorandum and (iii) are in compliance with all such certificates,
authorities, permits and other authorizations.  Neither the Company nor any of
its subsidiaries has received any written notice of proceedings relating to the
revocation or modification of any such certificate, authority, permit or other
authorization, other than any such revocation or modification that could not
reasonably be expected to, singly or in the aggregate, have a Material Adverse
Effect.

         (k)     The Company and its subsidiaries have good and defensible
title to all real property owned by the Company and its subsidiaries and good
title to all other properties owned by them, in each case, free and clear of
all mortgages, pledges, liens, security interests, claims, restrictions or
encumbrances of any kind except such as (a) are described in the Offering
Memorandum or (b) would not, singly or in the aggregate, have a Material
Adverse Effect; and all of the leases and subleases (excluding such interests
in oil and gas properties and similar industry property interests) material to
the business of the Company and its subsidiaries, considered as one enterprise,
and under which the Company or any of its subsidiaries holds properties
described in the Offering Memorandum, are in full force and effect, and neither
the Company nor any of its subsidiaries has any notice of any material claim of
any sort that has been asserted by anyone adverse to the rights of the Company
or any of its subsidiaries under any of the leases or subleases mentioned
above, or affecting or questioning the rights of such the Company or any
subsidiary thereof to the continued possession of the leased or subleased
premises under any such lease or sublease.

         (l)     The Company and each of its subsidiaries have timely filed all
United States federal income tax returns and all other material tax returns
which are required to be filed by them (except where the failure to so file any
such return could not reasonably be expected to have a Material Adverse Effect)
and have paid all taxes due and payable and any related assessments, fines or
penalties (other than taxes, assessments, fines or penalties, the payment of
which are being contested in good faith or the failure to pay which would not
have a Material





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Adverse Effect), and no tax liens have been filed and no claims are being
asserted with respect to any such taxes, which could reasonably be expected to
have a Material Adverse Effect.

         (m)     The present fair salable value of the assets of each of the
Company and the Subsidiary Guarantors exceed the amount that will be required
to be paid on or in respect of the existing debts and other liabilities
(including the maximum amount of liability that would reasonably be expected to
result from contingent liabilities) of the Company and the Subsidiary
Guarantors, respectively, as they mature; the respective assets of the Company
and the Subsidiary Guarantors do not constitute unreasonably small capital to
carry out their respective businesses as conducted or as proposed to be
conducted; neither the Company nor the Subsidiary Guarantors intend to, and do
not believe that they will, incur debts beyond their ability to pay such debts
as they mature; upon the issuance of the Notes and the Subsidiary Guarantees,
the present fair salable value of the assets of the Company and its
subsidiaries, taken as a whole, will exceed the amount that will be required to
be paid on or in respect of the existing debts and other liabilities (including
the maximum amount of liability that would reasonably be expected to result
from contingent liabilities) of the Company and its subsidiaries, taken as a
whole, as they mature; the assets of the Company and its subsidiaries, taken as
a whole, do not, and upon the issuance of the Notes and the Subsidiary
Guarantees will not, constitute unreasonably small capital for the Company and
its subsidiaries, taken as a whole, to carry out their respective business as
now conducted or as proposed to be conducted including the capital needs of the
Company and its subsidiaries, and projected capital requirements of the
business conducted by the Company and each of its subsidiaries, and projected
capital requirements and capital availability thereof; and neither the Company
nor the Subsidiary Guarantors intend to, and do not intend to permit any of
their subsidiaries to, incur debts beyond their respective ability to pay such
debts as they mature.

         (n)     The oil and gas reserve estimates of the Company and its
subsidiaries contained in the Offering Memorandum have been prepared by
independent petroleum consultants listed in the Offering Memorandum, and
neither the Company nor any of its subsidiaries has any reason to believe that
such estimates do not fairly reflect the oil and gas reserves of the Company
and its subsidiaries at the dates indicated.

         (o)     The Company and each of its subsidiaries have good and
defensible title to their respective interests in oil and gas properties, title
investigations having been carried out by or on behalf of the Company or its
subsidiaries in accordance with good practice in the oil and gas industry in
the areas in which they operate.

         (p)     The information provided by the Company or any of the
Subsidiaries to the Petroleum Consultants (as hereinafter defined) for the
preparation of the estimates of  reserves in the reserve reports for the oil and
gas properties of the Company prepared by H.J. Gruy and Associates, Inc., Harper
and Associates, Inc., Ryder Scott Company and Joe C. Neal & Associates,
independent petroleum consultants (collectively the "Petroleum Consultants"),
were at the respective times of delivery thereof to the Petroleum  Consultants
complete and accurate in all material respects.  The Purchasers have received a
true and correct copy of the reserve





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reports referred to in the Offering Memorandum under "Experts" (each a "Reserve
Report"), and each of the Reserve Reports and the letters from each of the
Petroleum Consultants to the Company with respect thereto have been reviewed,
and accepted as having a reasonable basis, by the Company.  The estimates of
reserves in the Reserve Reports were prepared in accordance with standard
geological and engineering methods generally accepted in the oil and gas
industry.

         (q)     There has been no storage, generation, transportation,
handling, treatment, disposal, discharge, emission, or other release of any
kind of toxic or other wastes or other hazardous substances, including, but not
limited to, brine, crude oil, natural gas liquids and other petroleum
materials, by, due to, or caused by the Company or any of its subsidiaries (or,
to the best of the Company's knowledge, any other entity for whose acts or
omissions the Company or any of its subsidiaries is or may be liable) upon any
of the property now or, to the best of the Company's knowledge, previously
owned or leased by the Company or any of its subsidiaries in violation of any
statute or any ordinance, rule, regulation, order, judgment, decree or permit
or which would, under any statute or any ordinance, rule (including rule of
common law), regulation, order, judgment, decree or permit, give rise to any
liability, except for any violation or liability which would not have,
singularly or in the aggregate with all such violations and liabilities, a
Material Adverse Effect; there has been no disposal, discharge, emission or
other release of any kind onto such property or into the environment
surrounding such property or any toxic or other wastes or other hazardous
substances with respect to which the Company or any of its subsidiaries have
knowledge, except for any such disposal, discharge, emission, or other release
of any kind which would not have, singularly or in the aggregate with all such
discharges and other releases, a Material Adverse Effect.

         (r)     As of the date hereof, (1) all royalties, rentals, deposits
and other amounts due on the oil and gas properties of and payable by the
Company and its subsidiaries have been properly and timely paid, and no
proceeds from the sale or production attributable to the oil and gas properties
of the Company and its subsidiaries are currently being held in suspense by any
purchaser thereof, except where such amount due could not, singly or in the
aggregate, have a Material Adverse Effect and (2) there are no claims under
take-or-pay contracts pursuant to which natural gas purchasers have any make-up
rights affecting the interest of the Company and its subsidiaries in its oil
and gas properties, except where such claims could not, singly or in the
aggregate, have a Material Adverse Effect.

         (s)     As of the date hereof, the aggregate undiscounted monetary
liability of the Company and its subsidiaries for petroleum taken or received
under any operating or gas balancing and storage agreement relating to its oil
and gas properties that permits any person to receive any portion of the
interest of the Company and its subsidiaries in any petroleum or to receive
cash or other payments to balance any disproportionate allocations of petroleum
could not, singly or in the aggregate, have a Material Adverse Effect.

         (t)     This Agreement has been duly authorized, executed and
delivered by the Company and the Subsidiary Guarantors.





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         (u)     The Indenture has been duly authorized by the Company and each
Subsidiary Guarantor and, when duly executed and delivered by the proper
officers of the Company and each Subsidiary Guarantor, will constitute a valid
and binding agreement of the Company and each Subsidiary Guarantor enforceable
against the Company and each Subsidiary Guarantor in accordance with its terms,
except as enforceability may be limited by bankruptcy, insolvency,
reorganization, moratorium and other similar laws relating to or affecting
creditors' rights generally, and by general equitable principles (regardless of
whether such enforceability is considered in a proceeding in equity or at law).

         (v)     The registration rights agreement to be dated as of the
Closing Date, among the Company, the Subsidiary Guarantors and the Purchasers
(the "Registration Rights Agreement") has been duly authorized by the Company
and each Subsidiary Guarantor and, when executed and delivered by the proper
officers of the Company and each Subsidiary Guarantor, will constitute a valid
and binding agreement of the Company and each Subsidiary Guarantor in
accordance with its terms, except as enforceability may be limited by
bankruptcy, insolvency, reorganization, moratorium and other similar laws
relating to or affecting creditors' rights generally, and by general equitable
principles (regardless of whether such enforceability is considered in a
proceeding in equity or at law).

         (w)     The Notes have been duly authorized by the Company and, when
duly executed, authenticated, issued and delivered as provided in the
Indenture, will be duly and validly issued and outstanding and will constitute
valid  and binding obligations of the Company entitled to the benefits of the
Indenture and enforceable in accordance with their terms, except as
enforceability may be limited by bankruptcy, insolvency, reorganization,
moratorium and other similar laws relating to or affecting creditors' rights
generally, and by general equitable principles (regardless of whether such
enforceability is considered in a proceeding in equity or at law); and the
Indenture and the Notes conform in all material respects to the descriptions
thereof contained in the Offering Memorandum.

         (x)     Each Subsidiary Guarantee has been duly authorized by each
Subsidiary Guarantor and, when duly executed, authenticated, issued and
delivered as provided in the Indenture and when the Notes have been issued and
authenticated in accordance with the terms of the Indenture and delivered to
and paid for by the Purchasers in accordance with the terms of this Agreement,
will be duly and validly issued and outstanding and will constitute valid and
binding obligations of each Subsidiary Guarantor entitled to the benefits of
the Indenture and enforceable in accordance with its terms, except as
enforceability may be limited by bankruptcy, insolvency, reorganization,
moratorium and other similar laws relating to or affecting creditors' rights
generally, and by general equitable principles (regardless of whether such
enforceability is considered in a proceeding in equity or at law).

         (y)     Neither the Company nor any of its subsidiaries is in
violation of its charter or by-laws or in default in the performance or
observance of any obligation, agreement, covenant or condition contained in any
contract, indenture, mortgage, deed of trust, loan or credit agreement, note,
lease or other agreement or instrument to which the Company or any of its
subsidiaries is





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a party or by which or any of them may be bound, or to which any of the
property or assets of the Company or any of its subsidiaries is subject
(collectively, "Agreements and Instruments") except for such defaults that
would not result in a Material Adverse Effect; and the execution, delivery and
performance of this Agreement, the Indenture and the Registration Rights
Agreement by the Company and each of the Subsidiary Guarantors, the Notes by
the Company, the Guarantees by each of the Subsidiary Guarantors and any other
agreement or instrument entered into or issued or to be entered into or issued
by the Company or the Subsidiary Guarantors in connection with the transactions
contemplated hereby or thereby or in the Offering Memorandum and the
consummation of the transactions contemplated herein and in the Offering
Memorandum (including the issuance and sale of the Notes and the use of the
proceeds from the sale of the Notes as described in the Offering Memorandum
under the caption "Use of Proceeds") and compliance by the Company with its
obligations hereunder will not, whether with or without the giving of notice or
passage of time or both, conflict with or constitute a breach of, or default or
a Repayment Event (as defined below) under, or result in the creation or
imposition of any lien, charge or encumbrance upon any property or assets of
the Company or any of its subsidiaries pursuant to, the Agreements and
Instruments except for such conflicts, breaches or defaults or liens, charges
or encumbrances that, singly or in the aggregate, would not result in a
Material Adverse Effect, nor will such action result in any violation of the
provisions of the charter or by-laws of the Company or any of its subsidiaries
or any applicable law, statute, rule, regulation, judgment, order, writ or
decree of any government, government instrumentality or court, domestic or
foreign, having jurisdiction over the Company or any of its subsidiaries or any
of their assets or properties.  As used herein, a "Repayment Event" means any
event or condition which gives the holder of any note, debenture or other
evidence of indebtedness (or any person acting on such holder's behalf) the
right to require the repurchase, redemption or repayment of all or a portion of
such indebtedness by the Company or any of its subsidiaries.

         (z)     No consent, approval, authorization or order of, or filing or
registration with, any court or governmental agency or body is required for the
execution, delivery and performance of this Agreement, the Indenture and the
Registration Rights Agreement by the Company and the Subsidiary Guarantors and
the Notes by the Company and the Subsidiary Guarantees by the Subsidiary
Guarantors and consummation of the transactions contemplated herein and
therein, except (i) such as may be required under foreign and Federal
securities laws and applicable state securities or "blue sky" laws in
connection with the purchase and distribution of the Notes by the Purchasers
(including a notice of sales on Form D pursuant to Rule 503 promulgated under
the Securities Act), (ii) the filing and effectiveness of a Registration
Statement as contemplated by the Registration Rights Agreement, (iii) such
approvals, registrations and qualifications as may be required under the
Securities Act, the Trust Indenture Act, and applicable state securities or
Blue Sky laws in connection with the exchange offer or resale registration
contemplated by the Offering Memorandum and set forth in the Registration
Rights Agreement, and (iv) such consents, approvals, authorizations,
registrations, filings or qualifications as may have been obtained or made or
of which the failure to obtain would not have a Material Adverse Effect.





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<PAGE>   9
         (aa)    The Company has not taken and will not take, directly or
indirectly, any action prohibited by Regulation M under the Exchange Act, in
connection with the offering of the Notes.

         (bb)    Neither the Company nor any affiliate (as defined in Rule
501(b) of Regulation D under the Securities Act ("Regulation D")) of the
Company has directly, or through any agent (provided that no representation is
made as to the Purchasers or any person acting on their behalf), (i) sold,
offered for sale, solicited offers to buy or otherwise negotiated in respect
of, any security (as defined in the Securities Act) which is or will be
integrated with the sale of the Notes in a manner that would require the
registration of the Notes under the Securities Act or (ii) engaged in any form
of general solicitation or general advertising (within the meaning of
Regulation D) in connection with the offering of the Notes.

         (cc)    It is not necessary in connection with the offer, sale and
delivery of the Notes to the Purchasers in the manner contemplated by this
Agreement to register the Notes under the Securities Act (provided that no
representation is made as to action of the Purchasers or persons acting on
their behalf) or to qualify the Indenture under the Trust Indenture Act of
1939, as amended (the "Trust Indenture Act").

         (dd)    Assuming (i) that the representations and warranties of the
Purchasers in Section 4 are true, and (ii) compliance by the Purchasers with
their covenants set forth in Section 4, it is not necessary in connection with
the initial resale of the Notes by the Purchasers in the manner contemplated by
this Agreement to register the Notes under the Securities Act.

         (ee)    The Notes satisfy the requirements set forth in Rule
144A(d)(3) under the Securities Act.

         (ff)    There is no "substantial U.S. market interest" as defined in
Rule 902(n) of Regulation S for the Notes or any security of the same class as
the Notes.

         (gg)    The Company, the Subsidiary Guarantors and their respective
affiliates and all persons acting on their behalf (other than the Purchasers
and their respective affiliates and all persons acting on their behalf, as to
whom the Company and the Subsidiary Guarantors make no representation) have
complied with and will comply with the "offering restrictions" requirements
(within the meaning of Regulation S) of Regulation S under the Securities Act
(including, without limitation, provisions regarding "directed selling efforts"
(within the meaning of Regulation S)) in connection with any offering of the
Notes outside the United States.

                 2.       Purchase and Sale.  Subject to the terms and
conditions and in reliance upon the representations, warranties and covenants
contained in this Agreement, the Company agrees to issue and sell to each of
the Purchasers, and each of the Purchasers agrees to purchase from the Company,
the principal amount of the Notes set forth opposite the name of such Purchaser
on Schedule I hereto at a purchase price of 97.0% of the principal amount
thereof plus accrued interest, if any, from July 7, 1998 to the Closing Date.





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                 3.       Delivery and Payment.  (a) Delivery of and payment
for the Notes shall be made at the offices of Mayer, Brown & Platt, 1675
Broadway, New York, New York 10019, at 9:00 AM, New York time, on July 7, 1998,
or such other date, time or location as shall be agreed upon by the Purchasers
and the Company (such date and time of delivery and payment for the Notes being
herein called the "Closing Date").  Payment of the purchase price shall be made
to the Company by wire transfer of same day funds to an account or accounts
specified by the Company at least one business day prior to the Closing Date,
against delivery to the Purchasers for the respective accounts of the
Purchasers of the Notes to be purchased by them.  Delivery of the Notes shall
be made at such location as the Purchasers shall reasonably designate at least
one business day in advance of the Closing Date.

         (b)     One or more of the Notes in the definitive global form,
registered in the name of Cede & Co., as nominee of the Depository Trust
Company ("DTC"), having an aggregate principal amount corresponding to the
aggregate principal amount of the Notes (collectively, the "Global Note"),
shall be delivered by the Company to the Purchasers (or as the Purchasers
direct), in each case with any transfer taxes thereon duly paid by the Company.
The Global Note shall be made available to the Purchasers for inspection not
later than 10:30 a.m., New York time, on the business day immediately preceding
the Closing Date.

                 4.       Offering of Notes; Restrictions on Transfer. The
several Purchasers propose to offer the Notes for resale upon the terms and
conditions set forth in this Agreement and the Offering Memorandum.  Each
Purchaser hereby represents, warrants to, and agrees with the Company that:

         (a)     It will offer and sell the Notes only (i) to persons who it
reasonably believes are QIBs in transactions meeting the requirements of Rule
144A, (ii) a limited number of institutional "accredited investors" (as defined
in rule 501(a)(1), (2), (3) or (7) under the Securities Act) and who, as
purchasers, have executed and delivered to the Purchasers copies of the letter
set forth in Annex A to the Offering Memorandum or (iii) outside the United
States to certain persons in reliance on Regulation S under the Securities Act
upon the terms and conditions set forth in Annex I to this Agreement;

         (b)     It is an institutional "accredited investor" (as defined in
Rule 501 under the Securities Act) or a QIB; and

         (c)     It will not offer or sell the Notes by any form of general
solicitation or general advertising, including but not limited to the methods
described in Rule 502(c) under the Securities Act.

                 5.       Agreements.  The Company agrees with the Purchasers
that:

         (a)     The Company will furnish to the Purchasers, without charge,
during the period mentioned in paragraph (c) below, as many copies of the
Preliminary Offering Memorandum and the Offering Memorandum and any supplements
and amendments thereto as the Purchasers may





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<PAGE>   11
reasonably request.  The Company will pay the expenses of printing or other
production of all documents relating to the offering.

         (b)     The Company will advise the Purchasers promptly of any
proposal to amend or supplement the Offering Memorandum and will not effect
such amendment or supplement without the prior consent of Nesbitt Burns
Securities Inc., which consent shall not be unreasonably withheld.

         (c)     If, at any time prior to the completion of the sale of the
Notes by the Purchasers, any event occurs as a result of which the Offering
Memorandum, as then amended or supplemented, would include any untrue statement
of a material fact or omit to state any material fact necessary to make the
statements therein in the light of the circumstances under which they were made
not misleading, or if it shall be necessary to amend or supplement the Offering
Memorandum to comply with applicable law, the Company promptly will notify the
Purchasers of the same and will prepare and provide to the Purchasers pursuant
to paragraph (a) of this Section 5 an amendment or supplement which will
correct such statement or omission or effect such compliance.

         (d)     The Company will use commercially reasonable efforts to
qualify the Notes for sale under the laws of such jurisdictions as the
Purchasers may reasonably designate, will use commercially reasonable efforts
to maintain such qualifications in effect so long as required for the sale of
the Notes.  The Company will promptly advise the Purchasers of the receipt by
the Company of any notification with respect to the suspension of the
qualification of the Notes for sale in any jurisdiction or the initiation or
threatening of any proceeding for such purpose.  Notwithstanding the foregoing,
the Company shall not be obligated to file any general consent to service of
process or to qualify as a foreign corporation in any jurisdiction in which it
is not so qualified or to subject itself to taxation in respect of doing
business in any jurisdiction in which it is not otherwise so subject.

         (e)     The Company will not solicit any offer to buy or offer or sell
the Notes by means of any form of general solicitation or general advertising
(within the meaning of Regulation D).

         (f)     None of the Company, its subsidiaries, its affiliates or any
person acting on behalf of any of them (other than the Purchasers and their
respective affiliates, as to whom this undertaking shall not be deemed to
apply) will engage in any directed selling efforts (as that term is defined in
Regulation S) with respect to the Notes offered and sold pursuant to Regulation
S, and the Company, its subsidiaries, its affiliates and each person acting on
behalf of any of them (other than the Purchasers and their respective
affiliates, as to whom this undertaking by the Company shall not be deemed to
apply) will comply with the offering restrictions of Regulation S with respect
to those Notes offered and sold pursuant thereto.

         (g)     The Company shall, during any period in the two years after
the Closing Date in which the Company and the Subsidiary Guarantors are not
subject to Section 13 or 15(d) of the





                                       11
<PAGE>   12
Exchange Act, make available, upon request, to any holder of such Notes in
connection with any sale thereof and any prospective purchaser of Notes from
such holder the information ("Rule 144A Information") specified in Rule
144A(d)(4) under the Securities Act.

         (h)     The Company will not, and will not permit any of its
subsidiaries to, resell any Notes which constitute "restricted securities"
under Rule 144 that have been acquired by any of them, otherwise than pursuant
to an effective registration statement under the Securities Act.

         (i)     Neither the Company nor any subsidiary will sell, offer for
sale or solicit offers to buy or otherwise negotiate in respect of any security
(as defined in the Securities Act) the offering of which security will be
integrated with the sale of the Notes in a manner which would require the
registration of the Notes under the Securities Act.

         (j)     The Company shall use commercial reasonable efforts in
cooperation with the Purchasers to permit the Notes to be eligible for
clearance and settlement through The Depository Trust Company, the Euroclear
System and Cedel Bank, societe anonyme.

         (k)     The Company will not, for a period of 90 days following the
date hereof, without the prior written consent of Nesbitt Burns Securities
Inc., offer, sell or contract to sell, or otherwise transfer or dispose of,
directly or indirectly, or announce the offering of, any debt securities issued
or guaranteed by the Company substantially similar to the Notes (other than the
securities offered pursuant to an Exchange Offer Registration Statement for the
Notes).

         (l)     The Company shall use its best efforts, in cooperation with
the Purchasers, to cause the Notes to be eligible for and designated for
trading on the PORTAL trading system of the National Association of Securities
Dealers, Inc.

                 6.       Conditions to the Obligations of the Purchasers.  The
obligations of the Purchasers to purchase the Notes under this Agreement are
subject to the satisfaction of each of the following conditions:

         (a)     All representations and warranties of the Company and the
Subsidiary Guarantors contained in this Agreement shall be true and correct on
the date hereof and on the Closing Date with the same force and effect as if
made on and as of the Closing Date.

         (b)     The Company shall have furnished to the Purchasers the
opinion(which opinion may state that it is governed by and shall be interpreted
in accordance with the Legal Opinion Accord of the ABA Section of Business Law
(1991)) of Haynes and Boone, LLP, counsel for the Company, dated the Closing
Date, in form and substance satisfactory to the Purchasers, to the effect that:

                 (i)      The Company has been duly incorporated and is validly
         existing as a corporation in good standing under the laws of the State
         of Delaware and has corporate





                                       12
<PAGE>   13
         power and authority to own, lease and operate its properties and to
         conduct its business as described in the Offering Memorandum.

                 (ii)     Each of the Subsidiary Guarantors has been duly
         incorporated and is validly existing as a corporation in good standing
         under the laws of its jurisdiction of organization and has corporate
         power and authority to own, lease and operate its properties and to
         conduct its business as described in the Offering Memorandum.

                 (iii)    The Company's authorized capitalization is as set
         forth in the Offering Memorandum, and all of the issued shares of
         capital stock of the Company have been duly and validly authorized and
         issued and are fully paid and nonassessable and conform in all
         material respects to the description thereof contained in the Offering
         Memorandum.

                 (iv)     All the outstanding shares of capital stock of each
         subsidiary of the Company have been duly and validly authorized and
         issued and are fully paid and nonassessable, and, except as otherwise
         set forth in the Offering Memorandum, all outstanding shares of
         capital stock of the subsidiaries are owned by the Company, either
         directly or through wholly owned subsidiaries free and clear of any
         security interests, claims, liens, encumbrances or any other claim of
         any third party.

                 (v)      To the knowledge of such counsel, except as disclosed
         in the Offering Memorandum, there is no action, suit, proceeding,
         inquiry or investigation before or by any court or governmental agency
         or body, domestic or foreign, now pending against or affecting the
         Company or any subsidiary thereof which might reasonably be expected
         to result in a Material Adverse Effect.

                 (vi)     This Agreement has been duly authorized, executed and
         delivered by the Company and the Subsidiary Guarantors.

                 (vii)    The Indenture has been duly authorized, executed and
         delivered by the Company and each Subsidiary Guarantor and constitutes
         a valid and binding agreement of the Company and each Subsidiary
         Guarantor enforceable against the Company and each Subsidiary
         Guarantor in accordance with its terms, except as enforceability may
         be limited by bankruptcy, insolvency, reorganization, moratorium and
         other similar laws relating to or affecting creditors' rights
         generally, and by general equitable principles (regardless of whether
         such enforceability is considered in a proceeding in equity or at
         law).

                 (viii)   The Registration Rights Agreement has been duly
         authorized, executed and delivered by the Company and each Subsidiary
         Guarantor and constitutes a valid and binding agreement of the Company
         and each Subsidiary Guarantor in accordance with its terms, except as
         enforceability may be limited by (A) bankruptcy, insolvency,
         reorganization, moratorium and other similar laws relating to or
         affecting creditors' rights generally, and by general equitable
         principles (regardless of whether such enforceability





                                       13
<PAGE>   14
         is considered in a proceeding in equity or at law) and (B) public
         policy considerations in respect of the enforceability of indemnity
         provisions.

                 (ix)     The Notes have been duly authorized, executed and
         delivered by the Company and (assuming the due authentication thereof
         by the Trustee) constitute valid  and binding obligations of the
         Company entitled to the benefits of the Indenture and enforceable in
         accordance with their terms, except as enforceability may be limited
         by bankruptcy, insolvency, reorganization, moratorium and other
         similar laws relating to or affecting creditors' rights generally, and
         by general equitable principles (regardless of whether such
         enforceability is considered in a proceeding in equity or at law); and
         the Indenture and the Notes conform in all material respects to the
         description thereof contained in the Offering Memorandum.

                 (x)      The Subsidiary Guarantee of each Subsidiary Guarantor
         has been duly authorized, executed and delivered by such Subsidiary
         Guarantor and when the Notes have been executed, authenticated and
         issued in accordance with the terms of the Indenture and delivered to
         and paid for by the Purchasers in accordance with this Agreement
         constitutes a valid and binding obligation of such Subsidiary
         Guarantor enforceable in accordance with its terms, except as
         enforceability may be limited by bankruptcy, insolvency,
         reorganization, moratorium and other similar laws relating to or
         affecting creditors' rights generally, and by general equitable
         principles (regardless of whether such enforceability is considered in
         a proceeding in equity or at law).

                 (xii)    The execution, delivery and performance of this
         Agreement, the Indenture and the Registration Rights Agreement by the
         Company and each of the Subsidiary Guarantors, the Notes by the
         Company, the Guarantees by each of the Subsidiary Guarantors and the
         consummation of the transactions contemplated herein (including the
         issuance and sale of the Notes and the use of the proceeds from the
         sale of the Notes as described in the Offering Memorandum under the
         caption "Use of Proceeds") and compliance by the Company with its
         obligations hereunder will not, whether with or without the giving of
         notice or passage of time or both, conflict with or constitute a
         breach of, or default or a Repayment Event (as defined below) under,
         or result in the creation or imposition of any lien, charge or
         encumbrance upon any property or assets of the Company or any of its
         subsidiaries pursuant to, any reviewed agreement (as delivered and
         defined in the opinion), except for such conflicts, breaches or
         defaults or liens, charges or encumbrances that, singly or in the
         aggregate, would not result in a Material Adverse Effect, nor will
         such action result in any violation of the provisions of the charter
         or by-laws of the Company or any of its subsidiaries or, breach or
         violated any court order, any applicable law, statute, rule,
         regulation, of any government, government instrumentality or court,
         domestic or foreign, having jurisdiction over the Company or any of
         its subsidiaries or any of their assets or properties and specifically
         applicable to the Company which violation or breach would have a
         Material Adverse Effect.  As used herein, a "Repayment Event" means
         any event or condition which gives the holder of any note, debenture
         or other evidence of indebtedness (or any person acting on such
         holder's





                                       14
<PAGE>   15
         behalf) the right to require the repurchase, redemption or repayment
         of all or a portion of such indebtedness by the Company or any of its
         subsidiaries.

                 (xiii)   No consent, approval, authorization or order of, or
         filing or registration with, any court or governmental agency or body
         is required for the execution, delivery and performance of this
         Agreement, the Indenture and the Registration Rights Agreement by the
         Company and the Subsidiary Guarantors and the Notes by the Company and
         the Subsidiary Guarantees by the Subsidiary Guarantors and
         consummation of the transactions contemplated herein and therein,
         except (A) as such may be required under foreign and United States
         Federal securities laws and applicable state securities or "blue sky"
         laws in connection with the purchase and distribution of the Notes by
         the Purchasers (including a notice of sales on Form D pursuant to Rule
         503 promulgated under the Securities Act), (B) the filing and
         effectiveness of a Registration Statement as contemplated by the
         Registration Rights Agreement, (C) such approvals, registrations and
         qualifications as may be required under the Securities Act, the Trust
         Indenture Act, and applicable state securities or Blue Sky laws in
         connection with the exchange offer or resale registration contemplated
         by the Offering Memorandum and set forth in the Registration Rights
         Agreement, and (D) such consents, approvals, authorizations,
         registrations, filings or qualifications as may have been obtained or
         made or of which the failure to obtain would not have a Material
         Adverse Effect.

                 (xiv)    Neither the registration of the Notes under the
         Securities Act, nor the qualification of an indenture under the Trust
         Indenture Act of 1939 with respect thereto, is required for the offer
         and sale of the Notes by the Company to the Purchasers or the reoffer
         and resale of the Notes by the Purchasers in the manner contemplated
         in this Agreement and the Offering Memorandum, other than any
         registration or qualification that may be required in connection with
         the Exchange Offer contemplated by the Offering Memorandum or in
         connection with the Registration Rights Agreement.

                 (xv)     The Company is not an "investment company" within the
         meaning of the Investment Company Act.

                 (xvi)    The statements in the Offering Circular under the
         captions "Description of Notes," "Description of Other Indebtedness,"
         "Description of Capital Stock," "Exchange Offer; Registration Rights"
         and "Certain U.S.  Federal Income Tax Considerations" insofar as such
         statements constitute summaries of the provisions of the Company's
         existing debt, the Notes, the Registration Rights Agreement, or
         insofar as such statements purport to summarize federal laws of the
         United States referred to thereunder, as the case may be, are accurate
         in all material respects.

         Such counsel shall also state that they examined various documents and
participated in conferences with representatives of the Company and its
accountants and with representatives of the Purchasers and their counsel at
which times the contents of the Offering Memorandum and related matters were
discussed.  However such counsel need not pass upon nor assume any





                                       15
<PAGE>   16
responsibility for the accuracy, completeness or fairness of the statements
contained in the Offering Memorandum (except as provided above) or make any
representation that such counsel has independently verified or checked the
accuracy, completeness or fairness of such statements.  Also, such counsel need
express no view as to the financial statements and other financial information
included or incorporated by reference in or excluded from the Offering
Memorandum.  Subject to the foregoing, such counsel shall advise the Purchasers
that no facts have come to such counsel's attention that causes it to believe
that the Offering Memorandum and any amendments or supplements thereto made by
the Company prior to the Closing Date, contained, as of its date, or contains,
as of the Closing Date, an untrue statement of a material fact or omitted as of
its date, or omits, as of the Closing Date, to state a material fact necessary
in order to make the statements therein, in light of the circumstances under
which they were made, not misleading.

         Such counsel's opinion shall be limited to the laws of the State of
Texas, the General Corporation Law of the State of Delaware and the federal law
of the United States of America  (it being understood, however, that with
respect to the validity, binding effect and enforceability of the Indenture,
the Notes and the Registration Rights Agreement, counsel may opine as if such
instruments were governed by the laws of the State of Texas).  In rendering
such opinion, such counsel shall be entitled to rely, as to certain matters, on
information contained in certificates of officers of the Company.

         (c)     The Purchasers shall have received from Mayer, Brown & Platt,
counsel for the Purchasers, such opinion or opinions, dated the Closing Date,
with respect to the issuance and sale of the Notes, the Indenture, the Offering
Memorandum (together with any amendment or supplement thereof or thereto) and
other related matters as the Purchasers may reasonably require, and the Company
shall have furnished to such counsel such documents as they request for the
purpose of enabling them to pass upon such matters.

         (d)     The Company shall have furnished to the Purchasers a
certificate of the Company, signed by the Chairman of the Board or the
President and the principal financial or accounting officer of the Company,
dated the Closing Date, to the effect that the signers of such certificate have
carefully examined the Offering Memorandum, any amendment or supplement to the
Offering Memorandum and this Agreement and that:

                          (i)     the representations and warranties of the
                 Company in this Agreement are true and correct in all material
                 respects on and as of the Closing Date with the same effect as
                 if made on the Closing Date and the Company has complied in
                 all material respects with all the agreements and satisfied
                 all the conditions on its part to be performed or satisfied at
                 or prior to the Closing Date; and

                          (ii)    since the date of the most recent financial
                 statements included or incorporated by reference in the
                 Offering Memorandum (exclusive of any amendment or supplement
                 thereof or thereto), there has been no material adverse





                                       16
<PAGE>   17
                 change, or any development which could reasonably be expected
                 to result in a material adverse change, in the business,
                 prospects, financial condition or results of operations of the
                 Company and its subsidiaries taken as a whole, whether or not
                 arising from transactions in the ordinary course of business,
                 except as set forth in or contemplated in the Offering
                 Memorandum (exclusive of any amendment or supplement thereof
                 or thereto).

         (e)     On the date hereof and on and at the Closing Date, Ernst &
Young LLP shall have furnished to the Purchasers a letter or letters, dated
respectively as of the date hereof and as of the Closing Date, in form and
substance reasonably satisfactory to the Purchasers, confirming that they are
independent accountants within the meaning of the Securities Act and the Rules
of Conduct of the American Institute of Certified Public Accountants and
containing statements and information of the type ordinarily included in
accountants' "comfort letters" to Initial Purchasers with respect to the
financial statements and certain financial information contained in the
Offering Memorandum.

         (f)     The Company shall have furnished to the Purchasers a letter
from each of the Petroleum Consultants dated the date of delivery thereof, in
form and substance satisfactory to the Purchasers, confirming that they are
independent petroleum consultants with respect to the Company and its
subsidiaries, attaching their report with respect to the Company's and its
subsidiaries oil and gas reserves and stating that as of the date of such
letter they have no reason to believe that the conclusions and findings of such
firm contained in such report are not true or correct (other than by reason of
changes in commodity prices since the date of the report).

         (g)     The Purchasers shall have received a letter (the "bring-down
letter") from each of the Petroleum Consultants, addressed to the Purchasers
and dated the Closing Date confirming, as of the Closing Date, the conclusions
and findings of such firm with respect to the information and other matters
covered by their letter delivered to the Purchasers pursuant to paragraph (f)
and confirming in all material respects the conclusions and findings set forth
in such prior letter.

         (h)     Subsequent to the date hereof or, if earlier, the dates as of
which information is given in the Offering Memorandum (exclusive of any
amendment or supplement thereof or thereto), there shall not have been any
material adverse change, or any development which could reasonably be expected
to result in a material adverse change, in the business, prospects, financial
condition or results of operations of the Company and its subsidiaries taken as
a whole, whether or not arising from transactions in the ordinary course of
business, except as set forth in or contemplated in the Offering Memorandum
(exclusive of any amendment or supplement thereof or thereto) the effect of
which is, in the judgment of the Purchasers so material and adverse as to make
it impracticable or inadvisable to proceed with the offering or the delivery of
the Notes on the terms and in the manner contemplated in this Agreement and the
Offering Memorandum.

         (i)     Subsequent to the date hereof, there shall not have been any
downgrading in the rating of any of the Company's debt securities by any
"nationally recognized statistical rating organization" (as defined for
purposes of Rule 436(g) under the Securities Act) or any written





                                       17
<PAGE>   18
notice given of any intended or potential downgrading in any such rating or of
a possible change in any such rating that does not indicate the direction of
the possible change.

         (j)     On the Closing Date, the Notes shall have been designated for
trading on PORTAL.

         (k)     Prior to or concurrently with the consummation of the
transaction contemplated hereby, the Company shall have consummated or shall
consummate the transactions contemplated by the Securities Purchase Agreement,
dated as of June 25, 1998, among the Company and the other parties thereto on
substantially the same terms as described in the Offering Memorandum under the
caption "Private Equity Placement."

         (l)     Prior to the Closing Date, the Company shall have furnished to
the Purchasers such further information, certificates and documents as the
Purchasers may reasonably request.

         If any of the conditions specified in this Section 6 shall not have
been fulfilled in all material respects when and as provided in this Agreement,
or if any of the opinions and certificates mentioned above or elsewhere in this
Agreement shall not be in all material respects reasonably satisfactory in form
and substance to the Purchasers and counsel for the Purchasers, this Agreement
and all obligations of the Purchasers hereunder may be canceled at, or at any
time prior to, the Closing Date by the Purchasers.  Notice of such cancellation
shall be given to the Company in writing or by telephone or telegraph confirmed
in writing.

                 7.       Reimbursement of Purchasers' Expenses.  If the sale
of the Notes provided for herein is not consummated because any condition to
the obligations of the Purchasers set forth in Section 6 hereof is not
satisfied, or because of any refusal, inability or failure on the part of the
Company to perform any agreement herein or comply with any provision hereof
other than by reason of a default by either Purchaser, the Company and the
Subsidiary Guarantors will reimburse the Purchasers upon demand for all
out-of-pocket expenses (including reasonable fees and disbursements of counsel)
that shall have been incurred by it in connection with the proposed purchase
and sale of the Notes and the Company and the Subsidiary Guarantors shall then
be under no further liability to any Purchaser except as provided in Section 8.

                 8.       Indemnification and Contribution.  (a)  The Company
and each Subsidiary Guarantor agree to indemnify and hold harmless the
Purchasers, the directors, officers, employees and agents of each Purchaser and
each person who controls any Purchaser within the meaning of either the
Securities Act or the Exchange Act, from and against any and all losses,
claims, damages or liabilities, joint or several, to which they or any of them
may become subject under the Securities Act, the Exchange Act or other Federal
or state statutory law or regulation, at common law or otherwise, insofar as
such losses, claims, damages or liabilities (or actions in respect thereof)
arise out of or are based upon any untrue statement or alleged untrue statement
of a material fact contained in the Offering Memorandum (or any amendment or
supplement thereto) or any Rule 144A Information provided by the Company to any
holder or prospective purchaser of Notes pursuant to Section 5(g), or arise out
of or are based upon the omission or





                                       18
<PAGE>   19
alleged omission to state therein a material fact required to be stated therein
or necessary to make the statements therein not misleading, and agrees to
reimburse each such indemnified party, as incurred, for any legal or other
expenses reasonably incurred by them in connection with investigating or
defending any such loss, claim, damage, liability or action; provided, however,
that the Company and the Subsidiary Guarantors will not be liable in any such
case to the extent that any such loss, claim, damage or liability arises out of
or is based upon any such untrue statement or alleged untrue statement or
omission or alleged omission made in the Offering Memorandum, or in any
amendment thereof or supplement thereto, in reliance upon and in conformity
with written information furnished to the Company by or on behalf of the
Purchasers relating to such Purchaser specifically for inclusion therein; and
provided, further, that the foregoing indemnity agreement with respect to the
Offering Memorandum shall not inure to the benefit of the Purchasers from whom
the person asserting or causing any such losses, claims, damages or liabilities
purchased Notes (or to the benefit of any person controlling any Purchaser or
any directors, officers, employees and agents of any Purchaser), if a copy of
the Offering Memorandum (or the Offering Memorandum as amended or supplemented)
(if the Company shall have timely furnished the Purchasers with sufficient
copies thereof) was not sent or given by or on behalf of the Purchasers to such
person at or prior to the written confirmation of the sale of the Notes to such
person and if the Offering Memorandum (or the Offering Memorandum as amended or
supplemented) would have cured the defect giving rise to such loss, claim,
damage or liability.  This indemnity agreement will be in addition to any
liability which the Company may otherwise have.

         (b)     The Purchasers agree to indemnify and hold harmless the
Company and the Subsidiary Guarantors, their respective directors, its
officers, and each person who controls the Company or the Subsidiary Guarantors
within the meaning of either the Securities Act or the Exchange Act, to the
same extent as the foregoing indemnity from the Company and the Subsidiary
Guarantors to the Purchasers, but only with reference to written information
relating to the Purchasers furnished to the Company by or on behalf of the
Purchasers specifically for inclusion in the Offering Memorandum or in any
amendment thereof or supplement thereto.  This indemnity agreement will be in
addition to any liability which the Purchasers may otherwise have.

         (c)     Promptly after receipt by an indemnified party under this
Section 8 of notice of the commencement of any action, such indemnified party
will, if a claim in respect thereof is to be made against the indemnifying
party under this Section 8, notify the indemnifying party in writing of the
commencement thereof; but the failure so to notify the indemnifying party (i)
will not relieve it from liability under paragraph (a) or (b) above unless and
to the extent it did not otherwise learn of such action and such failure
results in the forfeiture by the indemnifying party of substantial rights and
defenses and (ii) will not, in any event, relieve the indemnifying party from
any obligations to any indemnified party other than the indemnification
obligation provided in paragraph (a) or (b) above.  The indemnifying party
shall be entitled to appoint counsel of the indemnifying party's choice at the
indemnifying party's expense to represent the indemnified party in any action
for which indemnification is sought (in which case the indemnifying party shall
not thereafter be responsible for the fees and expenses of any separate counsel
retained by





                                       19
<PAGE>   20
the indemnified party or parties except as set forth below); provided, however,
that such counsel shall be reasonably satisfactory to the indemnified party.
Notwithstanding the indemnifying party's election to appoint counsel to
represent the indemnified party in an action, the indemnified party shall have
the right to employ separate counsel (including local counsel), and the
indemnifying party shall bear the reasonable fees, costs and expenses of such
separate counsel if (i) the use of counsel chosen by the indemnifying party to
represent the indemnified party would present such counsel with a conflict of
interest, (ii) the indemnified party shall have been advised by counsel that
there may be legal defenses available to the indemnified party and/or other
indemnified parties which are different from or additional to those available
to the indemnifying party, (iii) the indemnifying party shall not have employed
counsel satisfactory to the indemnified party to represent the indemnified
party within a reasonable time after notice of the institution of such action
or (iv) the indemnifying party shall authorize the indemnified party to employ
separate counsel at the expense of the indemnifying party.  An indemnifying
party will not, without the prior written consent (which consent shall not be
unreasonably withheld) of the indemnified parties, settle or compromise or
consent to the entry of any judgment with respect to any pending or threatened
claim, action, suit or proceeding in respect of which indemnification or
contribution may be sought hereunder (whether or not the indemnified parties
are actual or potential parties to such claim or action) unless such
settlement, compromise or consent includes an unconditional release of each
indemnified party from all liability arising out of such claim, action, suit or
proceeding.  No indemnifying party shall be liable for any settlement of any
such action effected without its written consent (which consent shall not be
unreasonably withheld), but if settled with its written consent or if there be
a final judgment for the plaintiff in any such action, the indemnifying party
agrees to indemnify and hold harmless any indemnified party from and against
any loss or liability by reason of such settlement of judgment.

         (d)     In the event that the indemnity provided in paragraph (a) or
(b) of this Section 8 is unavailable to or insufficient to hold harmless an
indemnified party for any reason, the Company and the Subsidiary Guarantors, on
the one hand, and the Purchasers, on the other hand, agree to contribute to the
aggregate losses, claims, damages and liabilities (including legal or other
expenses reasonably incurred in connection with investigating or defending
same) (collectively "Losses") to which the Company and the Subsidiary
Guarantors, on the one hand, and the Purchasers, on the other hand, may be
subject in such proportion as is appropriate to reflect the relative benefits
received by the Company and the Subsidiary Guarantors, on the one hand, and by
the Purchasers on the other hand, from the offering of the Notes; provided,
however, that in no case shall the Purchasers be responsible for any amount in
excess of the purchase discount or commission applicable to the Notes purchased
by the Purchasers hereunder.  If the allocation provided by the immediately
preceding sentence is unavailable for any reason, the Company and the
Subsidiary Guarantors, on the one hand, and the Purchasers, on the other hand,
shall contribute in such proportion as is appropriate to reflect not only such
relative benefits but also the relative fault of the Company and the Subsidiary
Guarantors, on the one hand, and of the Purchasers, on the other hand, in
connection with the statements or omissions which resulted in such Losses as
well as any other relevant equitable considerations.  Benefits received by the
Company and the Subsidiary Guarantors shall be deemed to be equal to the total
net proceeds from the offering (before deducting expenses), and benefits
received by the Purchasers





                                       20
<PAGE>   21
shall be deemed to be equal to the total purchase discounts and commissions, in
each case as set forth on the cover page of the Offering Memorandum.  Relative
fault shall be determined by reference to whether any alleged untrue statement
or omission relates to information provided by the Company or the Purchasers.
The Company and the Subsidiary Guarantors, on the one hand, and the Purchasers,
on the other hand, agree that it would not be just and equitable if
contribution were determined by pro rata allocation or any other method of
allocation which does not take account of the equitable considerations referred
to above.  Notwithstanding the provisions of this paragraph (d), no person
guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of
the Securities Act) shall be entitled to contribution from any person who was
not guilty of such fraudulent misrepresentation.  For purposes of this Section
8, each person who controls any Purchaser within the meaning of either the
Securities Act or the Exchange Act and each director, officer, employee and
agent of any Purchaser shall have the same rights to contribution as each
Purchaser, and each person who controls the Company or the Subsidiary
Guarantors within the meaning of either the Securities Act or the Exchange Act
and each officer and director of the Company and the Subsidiary Guarantors
shall have the same rights to contribution as the Company and the Subsidiary
Guarantors, subject in each case to the applicable terms and conditions of this
paragraph (d).

                 9.       Termination.  This Agreement shall be subject to
termination in the absolute discretion of the Purchasers, by written notice
given to the Company prior to delivery of and payment for the Notes, if prior
to such time any of the following events shall have occurred:  (i) any outbreak
or escalation of hostilities or other national or international calamity or
crisis or change in economic conditions or in the financial markets of the
United States or elsewhere that, in the Purchasers' good faith judgment, make
it impracticable to market the Notes on the terms and in the manner
contemplated in the Offering Memorandum; (ii) the suspension or material
limitation of trading in securities on the New York Stock Exchange, the
American Stock Exchange, the Chicago Board of Options Exchange, the Chicago
Mercantile Exchange, the Chicago Board of Trade or the Nasdaq National Market;
(iii) the suspension of trading of any securities of the Company on any
exchange or in the over-the-counter market; (iv) the enactment, publication,
decree or other promulgation of any federal or state statute, regulation, rule
or order of any court or other governmental authority which in the Purchasers'
good faith opinion materially and adversely affects, or will materially and
adversely affect, the business, prospects, financial condition or results of
operations of the Company and its subsidiaries, taken as a whole; (v) the
declaration of a banking moratorium by either federal or New York State
authorities or (vi) the taking of any action by any federal, state or local
government or agency in respect of its monetary or fiscal affairs which in the
Purchasers' good faith opinion has a material adverse effect on the financial
markets in the Unites States and would, in the Purchasers' good faith judgment,
make it impracticable to market the Notes on the terms and in the manner
contemplated in the Offering Memorandum.

                 10.      Representations and Indemnities to Survive.  The
respective agreements, representations, warranties, indemnities and other
statements of the Company, the Subsidiary Guarantors or their respective
officers and of the Purchasers set forth in or made pursuant to this Agreement
will remain in full force and effect, regardless of any investigation made by
or on





                                       21
<PAGE>   22
behalf of the Purchasers or the Company or the Subsidiary Guarantors or any of
the officers, directors or controlling persons referred to in Section 8 hereof,
and will survive delivery of and payment for the Notes.  The provisions of
Sections 7 and 8 hereof shall survive the termination or cancellation of this
Agreement.

                 11.      Notices.  All communications hereunder will be in
writing and effective only on receipt, and, if sent to the Purchasers, will be
mailed, delivered or sent by facsimile transmission and confirmed to them at
Nesbitt Burns Securities Inc., 111 West Monroe Street, Chicago, Illinois
60603, attention: legal department (facsimile: (312) 701-7711); or, if sent to
the Company, will be mailed, delivered or sent by facsimile transmission and
confirmed to it at Queen Sand Resources, Inc., 3500 Oak Lawn, Suite 380,
Dallas, Texas 75219, attention Chief Executive Officer (facsimile: (214)
521-9960).

                 12.      Successors.  This Agreement will inure to the benefit
of and be binding upon the parties hereto and their respective successors and
the officers and directors and controlling persons referred to in Section 8
hereof, and no other person will have any right or obligation hereunder.  No
purchaser of any Notes from any Purchaser should be deemed a successor or
assign by reason merely of such purchase.

                 13.      Applicable Law.  This Agreement will be governed by
and construed in accordance with the laws of the State of New York.





                        [Signatures appear on next page]





                                       22
<PAGE>   23
         If the foregoing is in accordance with your understanding of our
agreement, please sign and return to us the enclosed duplicate hereof,
whereupon this letter and your acceptance shall represent a binding agreement
between the Company, the Subsidiary Guarantors and the Purchasers.

                                              Very truly yours,

                                              QUEEN SAND RESOURCES, INC.


                                              By:   /s/ EDWARD J. MUNDEN       
                                                    --------------------------
                                                    Name:   Edward J. Munden
                                                    Title:  Chief Executive 
                                                             Officer, President
                                                             and Chairman of 
                                                             the Board


                                              QUEEN SAND RESOURCES, INC.,
                                                a Nevada corporation


                                              By:   /s/ EDWARD J. MUNDEN        
                                                    ----------------------------
                                                    Name:   Edward J. Munden
                                                    Title:  President


                                              CORRIDA RESOURCES, INC.


                                              By:   /s/ EDWARD J. MUNDEN       
                                                    ----------------------------
                                                    Name:   Edward J. Munden
                                                    Title:  President


                                              NORTHLAND OPERATING CO.


                                              By:   /s/ EDWARD J. MUNDEN       
                                                    ----------------------------
                                                    Name:   Edward J. Munden
                                                    Title:  President
<PAGE>   24
The foregoing Agreement is hereby
confirmed and accepted as of the
date first above written.

NESBITT BURNS SECURITIES INC.
CIBC OPPENHEIMER CORP.
SOCIETE GENERALE SECURITIES CORP.

BY:   NESBITT BURNS SECURITIES INC.



      By:    /s/ MARK A. ROCHE                     
             -------------------------------
             Name:   Mark A. Roche
             Title:  Managing Director




                                       24
<PAGE>   25
                                   SCHEDULE I



<TABLE>
                                                                                                               Principal
                                                                                                                Amount of
      Name of Initial Purchaser                                                                                  Notes   
      -------------------------                                                                               -----------
<S>                                                                                                         <C>
Nesbitt Burns Securities Inc.   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  $ 62,500,000
CIBC Oppenheimer Corp.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    50,000,000
Societe Generale Securities Corporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    12,500,000
                                                                                                            -------------
Total . . . . . . . .  . . .. . . . . . . . . . . . . . . . . . . . . . . .                                  $125,000,000
                                                                                                             ============
</TABLE>





                                       25
<PAGE>   26
                                                                         ANNEX I


      1.     The Notes have not been and will not be registered under the
Securities Act and may not be offered or sold within the United States or to,
or for the account or benefit of, U.S. persons except in accordance with
Regulation S under the Securities Act or pursuant to an exemption from the
registration requirements of the Securities Act.  Each Purchaser represents
that it has offered and sold the Notes, and will offer and sell the Notes (i)
as part of their distribution at any time and (ii) otherwise until 40 days
after the later of the commencement of the offering and the Time of Delivery,
only in accordance with Rule 903 of Regulation S or Rule 144A under the
Securities Act or to a limited number of institutional "accredited investors"
(as defined in rule 501(a)(1), (2), (3) or (7) under the Securities Act).
Accordingly, each Purchaser agrees that neither it, its affiliates nor any
persons acting on its or their behalf has engaged or will engage in any
directed selling efforts with respect to the Notes, and it and they have
complied and will comply with the offering restrictions requirement of
Regulation S.  Each Purchaser agrees that, at or prior to confirmation of sale
of Notes (other than a sale pursuant to Rule 144A or to an institutional
"accredited investor"), it will have sent to each distributor, dealer or person
receiving a selling concession, fee or other remuneration that purchases Notes
from it during the restricted period a confirmation or notice to substantially
the following effect:

             "The securities covered hereby have not been registered under the
      U.S. Securities Act of 1933 (the "Securities Act") and may not be offered
      and sold within the United States or to, or for the account or benefit
      of, U.S. persons (i) as part of their distribution at any time of (ii)
      otherwise until 40 days after the later of the commencement of the
      offering and the closing date, except in either case in accordance with
      Regulation S (or Rule 144A if available) under the Securities Act.  Terms
      used above have the meaning given to them by Regulation S."

Terms used in this paragraph have the meanings given to them by Regulation S.

      Each Purchaser further agrees that it has not entered and will not enter
into any contractual arrangement with respect to the distribution or delivery
of the Notes, except with its affiliates or with the prior written consent of
the Company.

      2.     Notwithstanding the foregoing, Notes may be offered, sold and
delivered by the Purchasers in the United States and to U.S. persons pursuant
to Section 4 of the Purchase Agreement to which this Annex I is attached
without delivery of the written statement required by paragraph 1 above.

      3.     Each Purchaser further represents and agrees that (i) it has not
offered or sold and will not offer or sell any Notes to persons in the United
Kingdom except to persons whose ordinary activities involve them in acquiring,
holding, managing or disposing of investments (as principal or agent) for the
purposes of their businesses or otherwise in circumstances which have not
resulted and will not result in an offer to the public in the United Kingdom 
within the meaning.



                                        
                                Annex I, Page 1
<PAGE>   27

of the Public Offers of Securities Regulations 1995, (b) it has
complied, and will comply, with all applicable provisions of the Financial
Services Act of 1986 of Great Britain with respect to anything done by it in
relation to the Notes in, from or otherwise involving the United Kingdom, and
(c) it has only issued or passed on and will only issue or pass on in the
United Kingdom any document received by it in connection with the issuance of
the Notes to a person who is of a kind described in Article 11(3) of the
Financial Services Act of 1986 (Investment Advertisements) (Exemptions) Order
1996 of Great Britain or is a person to whom the document may otherwise
lawfully be issued or passed on.

      4.     Each Purchaser agrees that it will not offer, sell or deliver any
of the Notes in any jurisdiction outside the United States except under
circumstances that will result in compliance with the applicable laws thereof,
and that it will take at its own expense whatever action is required to permit
its purchase and resale of the Notes in such jurisdictions.  Each Purchaser
understands that no action has been taken to permit a public offering in any
jurisdiction outside the United States where action would be required for such
purpose.  Each Purchaser agrees not to cause any advertisement of the Notes to
be published in any newspaper or periodical or posted in any public place and
not to issue any circular relating to the Notes, except in any such case with
Nesbitt Burns Securities Inc.'s express written consent and then only at its
own risk and expense.





                                Annex I, Page 2