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                                                                   Exhibit 10.16

                             COSTILLA ENERGY, INC.

                                  $80,000,000

                         10 1/4% SENIOR NOTES DUE 2006

                               PURCHASE AGREEMENT



                                           January 14, 1998



BT Alex. Brown Incorporated
Prudential Securities Incorporated
c/o BT Alex. Brown Incorporated
One Bankers Trust Plaza
130 Liberty Street
New York, New York  10006

Ladies and Gentlemen:

         Costilla Energy, Inc. (the "Company"), a Delaware corporation, hereby
confirms its agreement with you (the "Initial Purchasers"), as set forth below.

         1.      The Securities.  Subject to the terms and conditions herein
contained, the Company proposes to issue and sell to the Initial Purchasers
$80,000,000 aggregate principal amount of the Company's 10 1/4% Senior Notes
due 2006 (the "Securities").  The Securities are to be issued under an
indenture dated as of October 1, 1996, between the Company and State Street
Bank and Trust Company, as trustee (the "Trustee"), as amended by the
Supplemental Indenture to be dated as of January 16, 1998 between the Company
and the Trustee (as so amended, the "Indenture").

         The Securities will be offered and sold to you without being
registered under the Securities Act of 1933, as amended (the "Act"), in
reliance on exemptions therefrom.

         In connection with the sale of the Securities, the Company has
prepared a preliminary offering memorandum dated January 5 , 1998 (the
"Preliminary Memorandum") and a final offering memorandum dated January 14,
1998 (the "Final Memorandum," the Preliminary Memorandum and the Final
Memorandum each herein being referred to as a "Memorandum") setting forth or
including a description of the terms of the Securities, the terms of the
offering of the Securities, a description
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of the Company and any material developments relating to the Company occurring
after the date of the most recent historical financial statements included
therein.  Unless otherwise indicated, all references herein to the Preliminary
Memorandum or the Final Memorandum shall be deemed to include any documents
filed under the Securities Exchange Act of 1934, as amended, and the rules and
regulations thereunder (the "Exchange Act") which are incorporated by reference
therein.  As used herein, the term "Incorporated Documents" means the documents
which at the time are incorporated by reference in the Preliminary Offering
Memorandum or the Final Memorandum or any amendment or supplement thereto.

         The Initial Purchasers and their direct and indirect transferees of
the Securities will be entitled to the benefits of the Registration Rights
Agreement, substantially in the form attached hereto as Exhibit A (the
"Registration Rights Agreement"), pursuant to which the Company will agree,
among other things, to file a registration statement (the "Registration
Statement") with the Securities and Exchange  Commission (the "Commission")
registering the Exchange Notes (as defined in the Registration Rights
Agreement) under the Act.

         2.      Representations and Warranties of the Company.  The Company
represents and warrants to and agrees with each of the Initial Purchasers that:

                 (a)      Neither the Preliminary Memorandum as of the date
         thereof nor the Final Memorandum nor any amendment or supplement
         thereto as of the date thereof and at all times subsequent thereto up
         to the Closing Date (as defined in Section 3 below) contained or
         contains any untrue statement of a material fact or omitted or omits
         to state a material fact necessary to make the statements therein, in
         the light of the circumstances under which they were made, not
         misleading, except that the representations and warranties set forth
         in this Section 2(a) do not apply to statements or omissions made in
         reliance upon and in conformity with information relating to any of
         the Initial Purchasers furnished to the Company in writing by the
         Initial Purchasers expressly for use in the Preliminary Memorandum,
         the Final Memorandum or any amendment or supplement thereto.

                 (b)      The Incorporated Documents heretofore filed were
         filed in a timely manner and, when they were filed (or, if any
         amendment with respect to any such document was filed, when such
         amendment was filed), conformed in all material respects to the
         requirements of the Exchange Act and did not contain an untrue
         statement of a material fact or omit to state a material fact required
         to be stated therein or necessary to make the statements therein not
         misleading; and any further Incorporated Documents will, when so
         filed, be filed in a timely manner and conform in all material
         respects to the requirements of the Exchange Act and will not contain
         an untrue statement of a material fact or omit to state a material
         fact required to be stated therein or necessary to make the statements
         therein not misleading.

                 (c)      As of the Closing Date, the Company will have the
         authorized, issued and outstanding capitalization set forth in the
         Final Memorandum (other than any changes due to the repurchase of
         common stock pursuant to the Company's existing stock repurchase


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         program and the exercise of outstanding stock options); all of the
         outstanding shares of capital stock of the Company and each of its
         subsidiaries (each, a "Subsidiary" and collectively, the
         "Subsidiaries") have been, and as of the Closing Date will be, duly
         authorized and validly issued, are fully paid and nonassessable and
         were not issued in violation of any preemptive or similar rights;
         except as set forth in the Final Memorandum, all of the outstanding
         shares of capital stock of the Company and the Subsidiaries will be
         free and clear of all liens, encumbrances, equities and claims or
         restrictions on transferability (other than those imposed by the Act
         and the securities or "Blue Sky" laws of certain jurisdictions) or
         voting.

                 (d)      Each of the Company and the Subsidiaries is duly
         organized, validly existing and in good standing under the laws of its
         jurisdiction of organization and has all requisite corporate or other
         power and authority to own its properties and conduct its business as
         now conducted and as described in the Final Memorandum; each of the
         Company and the Subsidiaries is duly qualified to do business and is
         in good standing in all other jurisdictions where the ownership or
         leasing of its properties or the conduct of its business requires such
         qualification, except where the failure to be so qualified would not,
         individually or in the aggregate, have a material adverse effect on
         the general affairs, management, business, condition (financial or
         otherwise), prospects or results of operations of the Company and the
         Subsidiaries, taken as a whole (any such event, a "Material Adverse
         Effect").

                 (e)      The Company has all requisite corporate power and
         authority to execute, deliver and perform each of its obligations
         under the Securities, the Exchange Notes (as defined in the
         Registration Rights Agreement) and the Private Exchange Notes (as
         defined in the Registration Rights Agreement).  The Securities, when
         issued, will be in the form contemplated by the Indenture.  The
         Securities, the Exchange Notes and the Private Exchange Notes have
         each been duly and validly authorized by the Company and, when
         executed by the Company and authenticated by the Trustee in accordance
         with the provisions of the Indenture and, in the case of the
         Securities, when delivered to and paid for by the Initial Purchasers
         in accordance with the terms of this Agreement, will have been duly
         executed, issued and delivered and will constitute valid and legally
         binding obligations of the Company, entitled to the benefits of the
         Indenture, and enforceable against the Company in accordance with
         their terms, except that the enforcement thereof may be subject to (i)
         bankruptcy, insolvency, reorganization, fraudulent conveyance,
         moratorium or other similar laws now or hereafter in effect relating
         to creditors' rights generally, and (ii) general principles of equity
         and the discretion of the court before which any proceeding therefor
         may be brought (regardless of whether such enforcement is considered
         in a proceeding in equity or at law).

                 (f)      The Company has all requisite corporate power and
         authority to execute, deliver and perform its obligations under the
         Indenture.  The Indenture has been qualified under the Trust Indenture
         Act of 1939, as amended (the "TIA").  The Indenture has been duly and
         validly authorized by the Company and, when executed and delivered in
         accordance with





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         its terms (assuming the due authorization, execution and delivery by
         the Trustee), will have been duly executed and delivered and will
         constitute a valid and legally binding agreement of the Company,
         enforceable against the Company in accordance with its terms, except
         that the enforcement thereof may be subject to (i) bankruptcy,
         insolvency, reorganization, moratorium or other similar laws now or
         hereafter in effect relating to creditors' rights generally and (ii)
         general principles of equity and the discretion of the court before
         which any proceeding therefor may be brought (regardless of whether
         such enforcement is considered in a proceeding in equity or at law).

                 (g)      The Company has all requisite corporate power and
         authority to execute, deliver and perform its obligations under the
         Registration Rights Agreement.  The Registration Rights Agreement has
         been duly and validly authorized by the Company and, when executed and
         delivered by the Company (assuming due authorization, execution and
         delivery by the other parties thereto), will have been duly executed
         and delivered and will constitute a valid and legally binding
         agreement of the Company, enforceable against the Company in
         accordance with its terms, except that (A) the enforcement thereof may
         be subject to (i) bankruptcy, insolvency, reorganization, fraudulent
         conveyance, moratorium or other similar laws now or hereafter in
         effect relating to creditors' rights generally and (ii) general
         principles of equity and the discretion of the court before which any
         proceeding therefor may be brought (regardless of whether such
         enforcement is considered in a proceeding in equity or at law) and (B)
         any rights to indemnity or contribution thereunder may be limited by
         federal and state securities laws and public policy considerations.

                 (h)      The Company has all requisite corporate power and
         authority to execute, deliver and perform its obligations under this
         Agreement and to consummate the transactions contemplated hereby.
         This Agreement and the consummation by the Company of the transactions
         contemplated hereby have been duly and validly authorized by the
         Company.  This Agreement has been duly executed and delivered by the
         Company.

                 (i)      No consent, approval, authorization or order of any
         court or governmental agency or body, or third party is required for
         the performance of this Agreement by the Company or the consummation
         of the other transactions contemplated hereby, except such as have
         been obtained and such as may be required under state securities or
         "Blue Sky" laws in connection with the purchase and resale of the
         Securities by the Initial Purchasers.  Neither the Company nor any of
         the Subsidiaries is (i) in violation of its certificate of
         incorporation or bylaws, (ii) in breach or violation of any statute,
         judgment, decree, order, rule or regulation applicable to any of them
         or any of their respective properties or assets, except for any such
         breach or violation which would not, individually or in the aggregate,
         have a Material Adverse Effect, or (iii) in breach of or default under
         (nor has any event occurred which, with notice or passage of time or
         both, would constitute a default under) or in violation of any of the
         terms or provisions of any indenture, mortgage, deed of trust, loan
         agreement, note, lease, license, franchise agreement, permit,
         certificate, contract or other agreement or instrument to which any of
         them is a party or to which their respective





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         properties or assets are subject (collectively, "Contracts"), except
         for any such breach, default, violation or event which would not,
         individually or in the aggregate, have a Material Adverse Effect.

                 (j)      The execution, delivery and performance by the
         Company of this Agreement, the Indenture, the Securities, the Exchange
         Notes, the Private Exchange Notes and the Registration Rights
         Agreement and the consummation of the transactions contemplated hereby
         and thereby, and the fulfillment of the terms hereof and thereof, will
         not conflict with or constitute or result in a breach of or a default
         under (or an event which with notice or passage of time or both would
         constitute a default under) or violation of or cause an acceleration
         of any obligation under, or result in the imposition or creation of
         (or the obligation to create or impose) a lien on any property or
         assets of the Company or any Subsidiary with respect to (i) the terms
         or provisions of any Contract, except for any such conflict, breach,
         violation, default or event which would not, individually or in the
         aggregate, have a Material Adverse Effect, (ii) the certificate of
         incorporation or bylaws of the Company or any of the Subsidiaries, or
         (iii) (assuming compliance with all applicable state securities or
         "Blue Sky" laws and assuming the accuracy of the representations and
         warranties of the Initial Purchasers in Section 8 hereof) any statute,
         judgment, decree, order, rule or regulation of any court or
         governmental agency or body applicable to the Company, the
         Subsidiaries or any of their respective properties or assets, except
         for any such conflict, breach or violation which would not,
         individually or in the aggregate, have a Material Adverse Effect.

                 (k)      Each of the Indenture, the Securities, the Exchange
         Notes, the Private Exchange Notes and the Registration Rights
         Agreement conforms in all material respects to the description thereof
         in the Final Memorandum.

                 (l)      The consolidated financial statements of the Company
         and the related notes thereto included in the Final Memorandum present
         fairly in all material respects the financial position, results of
         operations and cash flows of the Company at the dates and for the
         periods to which they relate and have been prepared in accordance with
         generally accepted accounting principles applied on a consistent
         basis, except as otherwise stated therein, and comply as to form in
         all material respects with the applicable accounting requirements of
         the Act and the rules and regulations thereunder.  The summary and
         selected financial and statistical data included in the Final
         Memorandum present fairly in all material respects the information
         shown therein and have been prepared and compiled on a basis
         consistent with the audited financial statements included therein,
         except as otherwise stated therein, and comply as to form in all
         material respects with the applicable accounting requirements of the
         Act and the rules and regulations thereunder.  KPMG Peat Marwick LLP
         is an independent public accounting firm within the meaning of the
         Act.

                 (m)      (i) The pro forma financial statements (including the
         notes thereto) and other pro forma financial information included in
         the Final Memorandum (A) comply as to form





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         in all material respects with the applicable requirements of
         Regulation S-X promulgated under the Exchange Act, (B) have been
         prepared in accordance with the Commission's rules and guidelines with
         respect to pro forma financial statements and (C) have been properly
         computed on the bases described therein, and (ii) the assumptions used
         in the preparation of the pro forma financial statements and other pro
         forma financial information included in the Final Memorandum are
         reasonable and the adjustments used therein are appropriate to give
         effect to the transactions or circumstances referred to therein.

                 (n)      Except as described in the Final Memorandum, there is
         not pending or, to the best knowledge of the Company, threatened any
         action, suit, proceeding, inquiry or investigation to which the
         Company is a party, or to which any of its properties or assets are
         subject, before or brought by any court, arbitrator or governmental
         agency or body, which, if determined adversely to the Company or any
         such Subsidiary, would have a Material Adverse Effect, or which seeks
         to restrain, enjoin, prevent the consummation of or otherwise
         challenge the issuance or sale of the Securities to be sold hereunder
         or the consummation of the other transactions described in the Final
         Memorandum.

                 (o)      Each of the Company and the Subsidiaries owns or
         possesses adequate licenses or other rights to use all patents,
         trademarks, service marks, trade names, copyrights and know-how
         necessary to conduct the businesses now or proposed to be operated by
         it as described in the Final Memorandum, and neither the Company nor
         any of the Subsidiaries has received any notice of infringement of or
         conflict with (or knows of no such infringement of or conflict with)
         asserted rights of others with respect to any patents, trademarks,
         service marks, trade names, copyrights or know-how which, if such
         assertion of infringement or conflict were sustained, would,
         individually or in the aggregate, have a Material Adverse Effect.

                 (p)      Each of the Company and the Subsidiaries possesses
         all licenses, permits, certificates, consents, orders, approvals and
         other authorizations from, and has made or will have made all
         declarations and filings with, all federal, state, local and other
         governmental authorities, all self-regulatory organizations and all
         courts and other tribunals presently required or necessary to own or
         lease, as the case may be, and to operate its properties and to carry
         on its business as now or proposed to be conducted as set forth in the
         Final Memorandum ("Permits"), except where the failure to obtain such
         Permits would not, individually or in the aggregate, have a Material
         Adverse Effect; each of the Company and the Subsidiaries has fulfilled
         and performed all of its obligations with respect to such Permits and
         no event has occurred which allows, or after notice or lapse of time
         would allow, revocation or termination thereof or results in any other
         material impairment of the rights of the holder of any such Permit,
         except for the lack of performance under, or the revocation or
         termination of, any Permit which would not, individually or in the
         aggregate, have a Material Adverse Effect; and neither the Company nor
         any Subsidiary has received any notice of any proceeding relating to
         revocation or modification of any such Permit, except





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         as described in the Final Memorandum and except where such revocation
         or modification would not, individually or in the aggregate, have a
         Material Adverse Effect.

                 (q)      Since the respective dates as of which information is
         given in the Final Memorandum and except as described therein, there
         has been no material adverse change, or any fact known to the Company
         which could reasonably be  expected to result in a material adverse
         change, in the general affairs, management, business, condition
         (financial or otherwise) 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, or any loss of, or
         damage to, properties (whether  or not insured) which could reasonably
         be expected to affect  materially and adversely the general affairs,
         management, business, condition (financial or otherwise) or  results
         of operations of the Company and its Subsidiaries taken  as a whole.
         Since the date of the latest balance sheet presented in the Final
         Memorandum, except as  expressly disclosed in the Final Memorandum,
         neither the Company nor any of its Subsidiaries has (i) incurred or
         undertaken any liabilities or  obligations, direct or contingent, that
         are material to the Company and its Subsidiaries taken as a whole,
         (ii) entered into any material transaction not in the ordinary course
         of business and consistent with past practice or (iii) declared or
         paid any dividend or made any distribution on any shares of its
         capital  stock or redeemed, purchased or otherwise acquired or agreed
         to  redeem, purchase or otherwise acquire any shares of its capital
         stock (other than any dividends or distributions to the Company).

                 (r)      Each of the Company and Subsidiaries has filed all
         necessary federal, state and foreign income and franchise tax returns,
         except where the failure to so file such returns would not,
         individually or in the aggregate, have a Material Adverse Effect, and
         has paid all taxes shown as due thereon.  Other than tax deficiencies
         which the Company or any of the Subsidiaries is contesting in good
         faith and for which the Company or such Subsidiary has provided
         adequate reserves, there are no tax deficiencies that have been
         asserted against the Company or any Subsidiary that would have,
         individually or in the aggregate, a Material Adverse Effect.

                 (s)      None of the Company or any of the Subsidiaries or any
         agent acting on their behalf has taken or will take any action that
         might cause this Agreement or the sale of the Securities to violate
         Regulation G, T, U or X of the Board of Governors of the Federal
         Reserve System, in each case as in effect, or as the same may
         hereafter be in effect, on the Closing Date.

                 (t)      Each of the Company and the Subsidiaries has good and
         defensible title to all property (including interests in oil and gas
         leases) described in the Final Memorandum as being owned by it free
         and clear of all liens, charges, encumbrances or restrictions, except
         as described in the Final Memorandum or to the extent the failure to
         have such title or the existence of such liens, charges, encumbrances
         or restrictions would not have, individually or in the aggregate, a
         Material Adverse Effect.  All leases (other than interests in oil and
         gas





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         leases), contracts and agreements to which the Company or any
         Subsidiary is a party or by which the Company or such Subsidiary is
         bound are valid and enforceable against the Company or such Subsidiary
         and, to the knowledge of the Company, are valid and enforceable
         against the other party or parties thereto and are in full force and
         effect with only such exceptions as would not have, individually or in
         the aggregate, a Material Adverse Effect.

                 (u)      There are no legal or governmental proceedings
         involving or affecting the Company, any of the Subsidiaries  or any of
         their respective properties or assets that would be required to be
         described in a prospectus pursuant to the Act that are not described
         in the Final Memorandum, nor are there any material contracts or other
         documents that would be required to be described in a prospectus
         pursuant to the Act that are not described in the Final Memorandum.

                 (v)      Except as would not, individually or in the
         aggregate, have a Material Adverse Effect, (A) each of the Company and
         the Subsidiaries is in compliance with and not subject to liability
         under applicable Environmental Laws, (B) each of the Company and the
         Subsidiaries has made all filings and provided all notices required
         under any applicable Environmental Law, and has in full force and
         effect and is in compliance with all Permits required under any
         applicable Environmental Laws, (C) there is no civil, criminal or
         administrative action, suit, demand, claim, hearing, notice of
         violation, investigation, proceeding, notice or demand letter or
         request for information pending or, to the knowledge of the Company,
         threatened against the Company or any Subsidiary under any
         Environmental Law, (D) no lien, charge, encumbrance or restriction has
         been recorded under any Environmental Law with respect to any assets,
         facility or property owned, operated, leased or controlled by the
         Company or any Subsidiary, (E) neither the Company nor any Subsidiary
         has received notice that it has been identified as a potentially
         responsible party under the Comprehensive Environmental Response,
         Compensation and Liability Act of 1980, as amended ("CERCLA"), or any
         comparable state law, and (F) no property or facility of the Company
         or any Subsidiary is (i)  listed or proposed for listing on the
         National Priorities List under CERCLA or (ii) listed in the
         Comprehensive Environmental Response, Compensation, Liability
         Information System List promulgated pursuant to CERCLA, or on any
         comparable list maintained by any state or local governmental
         authority.

                 For purposes of this Agreement, "Environmental Laws" means the
         common law and all applicable federal, state and local laws or
         regulations, codes, orders, decrees, judgments or injunctions issued,
         promulgated, approved or entered thereunder, relating to pollution or
         protection of public or employee health and safety or the environment,
         including, without limitation, laws relating to (i) emissions,
         discharges, releases or threatened releases of hazardous materials,
         into the environment (including, without limitation, ambient air,
         surface water, groundwater, land surface or subsurface strata), (ii)
         the manufacture, processing, distribution, use, generation, treatment,
         storage, disposal, transport or handling of hazardous





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         materials, and (iii) underground and aboveground storage tanks, and
         related piping, and emissions, discharges, releases or threatened
         releases therefrom.

                 (w)      There is no strike, labor dispute, slowdown or work
         stoppage with the employees of the Company or the Subsidiaries which
         is pending or, to the knowledge of the Company, threatened.

                 (x)      Each of the Company and the Subsidiaries carries
         insurance in such amounts and covering such risks in such amounts as
         are prudent and customary in the businesses in which they are engaged.

                 (y)      Neither the Company nor any Subsidiary has any
         liability for any prohibited transaction or funding deficiency or any
         complete or partial withdrawal liability with respect to any pension,
         profit sharing or other plan which is subject to the Employee
         Retirement Income Security Act of 1974, as amended ("ERISA"), to which
         the Company or any Subsidiary makes or ever has made a contribution
         and in which any employee of the Company or any Subsidiary is or has
         ever been a participant.  With respect to such plans, each of the
         Company and the Subsidiaries is in compliance in all material respects
         with all applicable provisions of ERISA.

                 (z)      Each of the Company and the Subsidiaries (i) makes
         and keeps books and records which are accurate in all material
         respects and (ii) maintains internal accounting controls which provide
         reasonable assurance that (A) transactions are executed in accordance
         with management's authorization, (B) transactions are recorded as
         necessary to permit preparation of its financial statements and to
         maintain accountability for its assets, (C) access to its assets is
         permitted only in accordance with management's authorization and (D)
         the reported accountability for its assets is compared with existing
         assets at reasonable intervals.

                 (aa)     Neither the Company nor any Subsidiary will be an
         "investment company" or "promoter" or "principal underwriter" for an
         "investment company," as such terms are defined in the Investment
         Company Act of 1940, as amended, and the rules and regulations
         thereunder.

                 (bb)     No holder of securities of the Company (other than
         the Registrable Notes (as defined in the Registration Rights
         Agreement)) will be entitled to have such securities registered under
         the registration statements required to be filed by the Company
         pursuant to the Registration Rights Agreement.

                 (cc)     Immediately after the consummation of the
         transactions contemplated by this Agreement, the fair value and
         present fair saleable value of the assets of each of the Company and
         the Subsidiaries will exceed the sum of its stated liabilities and
         identified contingent liabilities; neither the Company nor any of the
         Subsidiaries is, or will be after giving effect to the execution,
         delivery and performance of this Agreement and the





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         consummation of the transactions contemplated hereby, (a) left with
         unreasonably small capital with which to carry on its business as it
         is proposed to be conducted, (b) unable to pay its debts (contingent
         or otherwise) as they mature, or (c) otherwise insolvent.

                 (dd)     Neither the Company nor any of the Subsidiaries nor
         any of their respective Affiliates (as defined in Rule 501(b) of
         Regulation D under the Act) has directly, or through any agent, (i)
         sold, offered for sale, solicited offers to buy or otherwise
         negotiated in respect of any "security" (as defined in the Act) which
         is or could be integrated with the sale of the Securities in a manner
         that would require the registration under the Act of the Securities or
         (ii) engaged in any form of general  solicitation or general
         advertising (as those terms are used in Regulation D under the Act) in
         connection with the offering of the Securities or in any manner
         involving a public offering within the meaning of Section 4(2) of the
         Act.

                 (ee)     Assuming the accuracy of the representations and
         warranties of the Initial Purchasers in Section 8 hereof, it is not
         necessary in connection with the offer, sale and delivery of the
         Securities to the Initial Purchasers in the manner contemplated by
         this Agreement to register any of the Securities under the Act or to
         qualify the Indenture under the TIA.

                 (ff)     No securities of the Company are of the same class
         (within the meaning of Rule 144A under the Act) as the Securities and
         listed on a national securities exchange registered under Section 6 of
         the Exchange Act, or quoted in a U.S. automated inter-dealer quotation
         system.

                 (gg)     Neither the Company nor any Subsidiary has taken, nor
         will take, directly or indirectly, any action designed to, or that
         might be reasonably expected to, cause or result in stabilization or
         manipulation of the price of the Securities.

                 (hh)     Neither the Company nor the Subsidiaries, nor any of
         their respective Affiliates (as defined in Rule 501(b) of Regulation D
         under the Act) or any person acting on any of their behalf (other than
         the Initial Purchasers as to which the Company and the Subsidiaries
         make no representation) has engaged in any directed selling efforts
         (as that term is defined in Regulation S under the Act ("Regulation
         S")) with respect to the Securities; the Company and its respective
         Affiliates and any person acting on any of their behalf (other than
         the Initial Purchasers as to which the Company and the Subsidiaries
         make no representation) have complied with the offering restrictions
         requirement of Regulation S.

         Any certificate signed by any officer of the Company or any Subsidiary
and delivered to any Initial Purchaser or to counsel for the Initial Purchasers
shall be deemed a joint and several representation and warranty by the Company
and each of the Subsidiaries to each Initial Purchaser as to the matters
covered thereby.





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         3.      Purchase, Sale and Delivery of the Securities.  On the basis
of the representations, warranties, agreements and  covenants herein contained
and subject to the terms and conditions herein set forth, the Company agrees to
issue and sell to the Initial Purchasers, and each of the Initial Purchasers
agrees, acting severally and not jointly, to purchase the Securities, at
100.25% of their principal amount, in the respective principal amounts set
forth opposite their names on Schedule I hereto.

         One or more certificates in definitive form for the Securities that
the Initial Purchasers have agreed to purchase hereunder, and in such
denomination or denominations and registered in such name or names as the
Initial Purchasers request upon notice to the Company at least 48 hours prior
to the Closing Date, shall be delivered by or on behalf of the Company to the
Initial Purchasers, against payment by or on behalf of the Initial Purchasers
of the purchase price therefor by wire transfer of immediately available funds
payable to such account or account as the Company shall specify prior to the
Closing Date, or by such means as the parties hereto shall agree prior to the
Closing Date.  Such delivery of and payment for the Securities shall be made at
the offices of Cahill Gordon & Reindel, 80 Pine Street, New York, New York, at
10:00 A.M., New York time, on January 16, 1998, or at such other place, time or
date as the Initial Purchasers and the Company may agree upon, such time and
date of delivery against payment being herein referred to as the "Closing
Date."  The Company will make such certificate or certificates for the
Securities available for checking and packaging by the Initial Purchasers at
the offices of BT Alex. Brown Incorporated in New York, New York or such other
place as BT Alex. Brown Incorporated may designate, at least 24 hours prior to
the Closing Date.

         4.      Offering by the Initial Purchasers.  The Initial Purchasers
propose to make an offering of the Securities at the price and upon the terms
set forth in the Final Memorandum as soon as practicable after this Agreement
is entered into and as in the sole judgment of the Initial Purchasers is
advisable.

         5.      Covenants of the Company.  The Company covenants and agrees
with each of the Initial Purchasers that:

                 (a)      The Company will not amend or supplement the Final
         Memorandum or any amendment or supplement thereto of which the Initial
         Purchasers and counsel to the Initial Purchasers shall not previously
         have been advised and furnished a copy for a reasonable period of time
         prior to the proposed amendment or supplement and as to which the
         Initial Purchasers shall not have given their consent, which consent
         shall not be unreasonably withheld.  The Company will promptly, upon
         the reasonable request of the Initial Purchasers or counsel for the
         Initial Purchasers, make any amendments or supplements to the
         Preliminary Memorandum or the Final Memorandum that may be necessary
         or advisable in connection with the resale of the Securities by the
         Initial Purchasers (but in no event longer than 180 days after the
         Closing Date).





                                       11
<PAGE>   12
                 (b)      The Company will cooperate with the Initial
         Purchasers in arranging for the qualification of the Securities for
         offering and sale under the securities or "Blue Sky" laws of such
         jurisdictions as the Initial Purchasers may designate and will
         continue such qualification in effect for as long as may be necessary
         to complete the resale of the Securities by the Initial Purchasers
         (but in no event longer than 180 days after the Closing Date);
         provided, however, that in connection therewith the Company shall not
         be required to qualify as a foreign corporation or to execute a
         general consent to service of process in any jurisdiction or subject
         the Company to any tax in any such jurisdiction where it is not then
         so subject.

                 (c)      If, at any time prior to the completion of the
         distribution by the Initial Purchasers of the Securities or the
         Private Exchange Notes, any event occurs or information becomes known
         as a result of which the Final Memorandum as then amended or
         supplemented would include an untrue statement of a material fact, or
         omit to state a material fact necessary to make the statements
         therein, in the light of the circumstances under which they were made,
         not misleading, or if for any other reason it is necessary at any time
         to amend or supplement the Final Memorandum in order to comply with
         applicable law, the Company will promptly notify the Initial
         Purchasers thereof and will prepare, at the Company's expense, an
         amendment to the Final Memorandum that corrects such statement or
         omission or effects such compliance.

                 (d)      The Company will, without charge, provide to the
         Initial Purchasers and to counsel for the Initial Purchasers as many
         copies of the Preliminary Memorandum and the Final Memorandum or any
         amendment or supplement thereto as the Initial Purchasers may
         reasonably request.

                 (e)      The Company will apply the net proceeds from the sale
         of the Securities substantially as set forth under "Use of Proceeds"
         in the Final Memorandum.

                 (f)      For so long as any Securities remain outstanding, the
         Company will upon request furnish to the Initial Purchasers copies of
         all reports and other communications (financial or otherwise)
         furnished by the Company to the Trustee or the holders of the
         Securities and, as soon as available, copies of any reports or
         financial statements furnished to or filed by the Company with the
         Commission or any national securities exchange on which any class of
         securities of the Company may be listed.

                 (g)      Prior to the Closing Date, the Company will furnish
         to the Initial Purchasers, as soon as they have been prepared by or
         are available to the Company, a copy of any unaudited interim
         consolidated financial statements of the Company for any period
         subsequent to the period covered by its most recent financial
         statements appearing in the Final Memorandum.





                                       12
<PAGE>   13
                 (h)      Neither the Company nor any of its Affiliates will
         sell, offer for sale or solicit offers to buy or otherwise negotiate
         in respect of any "security" (as defined in the Act) that could be
         integrated with the sale of the Securities in a manner that would
         require the registration under the Act of the Securities.

                 (i)      The Company will not, and will not permit any of the
         Subsidiaries to, engage in any form of general solicitation or general
         advertising (as those terms are used in Regulation D under the Act) in
         connection with the offering of the Securities or in any manner
         involving a public offering within the meaning of Section 4(2) of the
         Act.

                 (j)      For so long as any of the Securities remain
         outstanding, the Company will make available, upon request, to any
         holder of such Securities and any prospective purchasers thereof the
         information specified in Rule 144A(d)(4) under the Act, unless the
         Company is then subject to Section 13 or 15(d) of the Exchange Act.

                 (k)      The Company will use its best efforts to (i) permit
         the Securities to be designated PORTAL securities in accordance with
         the rules and regulations adopted by the NASD relating to trading in
         the Private Offerings, Resales and Trading through Automated Linkages
         market (the "PORTAL Market") and (ii) permit the Securities to be
         eligible for clearance and settlement through The Depository Trust
         Company.

         6.      Expenses.  The Company agrees to pay all costs and expenses
incident to the performance of its obligations under this Agreement, whether or
not the transactions contemplated herein are consummated or this Agreement is
terminated pursuant to Section 11 hereof, including all costs and expenses
incident to:  (i) the printing, word processing or other production of
documents with respect to such transactions, including any costs of printing
the Preliminary Memorandum and the Final Memorandum and any amendments or
supplements thereto, and any "Blue Sky" memoranda, (ii) all arrangements
relating to the delivery to the Initial Purchasers of copies of the foregoing
documents, (iii) the fees and disbursements of the counsel, the accountants and
any other experts or advisors retained by the Company, (iv) the preparation
(including printing), issuance and delivery to the Initial Purchasers of any
certificates evidencing the Securities, (v) the qualification of the Securities
under state securities and "Blue Sky" laws, including filing fees and
reasonable fees and disbursements of counsel for the Initial Purchasers
relating thereto, (vi) the expenses of the Company in connection with any
meetings with prospective investors in the Securities, (vii) the fees and
expenses of the Trustee, including fees and expenses of its counsel, and (viii)
all expenses and listing fees incurred in connection with the application for
quotation of the Securities on the PORTAL Market, (ix) any fees charged by
investment rating agencies for the rating of the Securities, and (x) all
reasonable out-of-pocket expenses of the Initial Purchasers incurred in
connection with the transactions contemplated hereby.

         7.      Conditions of the Initial Purchasers' Obligations.  The
obligation of the Initial Purchasers to purchase and pay for the Securities
shall, in their sole discretion, be subject to the satisfaction or waiver of
the following conditions on or prior to the Closing Date:





                                       13
<PAGE>   14
                 (a)      On the Closing Date, the Initial Purchasers shall
         have received the opinion, dated as of the Closing Date and addressed
         to the Initial Purchasers, of Cotton, Bledsoe, Tighe & Dawson, a
         Professional Corporation, counsel for the Company, in form and
         substance satisfactory to counsel for the Initial Purchasers, to the
         effect that:

                                   (i)  The Company and each of the
                 Subsidiaries is duly organized or incorporated, validly
                 existing and in good standing under the laws of its
                 jurisdiction of incorporation and has all requisite corporate
                 or other power and authority to own, lease and operate its
                 properties and to conduct its business as described in the
                 Final Memorandum.  Each of the Company and the Material
                 Subsidiaries is duly qualified as a foreign corporation or
                 limited liability company and in good standing in each
                 jurisdiction where the ownership or leasing of its properties
                 or the conduct of its business requires such qualification,
                 except where the failure to be so qualified would not have,
                 individually or in the aggregate, a Material Adverse Effect.

                                  (ii)  The Company has the authorized
                 capitalization set forth in the Final Memorandum; all of the
                 outstanding shares of capital stock of the Subsidiaries are
                 owned, directly or indirectly, by the Company, free and clear
                 of all perfected security interests, other than security
                 interests granted to the lenders under the Company's existing
                 secured credit facility, and, to the knowledge of such
                 counsel, free and clear of all other liens, encumbrances,
                 equities and claims or restrictions on transferability (other
                 than those imposed by the Act and the securities or "Blue Sky"
                 laws of certain jurisdictions) or voting.

                                 (iii)  No holder of securities of the Company
                 or any Subsidiary (other than the Registrable Notes) is
                 entitled to have such securities registered under a
                 registration statement filed by the Company pursuant to the
                 Registration Rights Agreement.

                                  (iv)  The Company has all requisite corporate
                 power and authority to execute, deliver and perform its
                 obligations under this Agreement and to consummate the
                 transactions contemplated hereby; this Agreement and the
                 consummation by the Company of the transactions contemplated
                 hereby have been duly and validly authorized by the Company.
                 This Agreement has been duly executed and delivered by the
                 Company.

                                   (v)  The Indenture (assuming the due
                 authorization, execution and delivery thereof by the Trustee),
                 constitutes the valid and legally binding agreement of the
                 Company, enforceable against the Company in accordance with
                 its terms, except that the enforcement thereof may be subject
                 to (i) bankruptcy, insolvency, reorganization, fraudulent
                 conveyance, moratorium or other similar laws now or hereafter
                 in effect relating to creditors' rights generally and (ii)
                 general principles of equity and the discretion of the court
                 before which any proceeding therefor may be





                                       14
<PAGE>   15
                 brought (regardless of whether such enforcement is considered
                 in a proceeding in equity or at law).  The Indenture has been
                 qualified under the TIA.

                                  (vi)  The Securities are in the form
                 contemplated by the Indenture.  The Securities have each been
                 duly and validly authorized, executed and delivered by the
                 Company.  The Securities, when paid for by the Initial
                 Purchasers in accordance with the terms of this Agreement
                 (assuming the due authorization, execution and delivery of the
                 Indenture by the Trustee and due authentication and delivery
                 of the Securities by the Trustee in accordance with the
                 Indenture), will constitute the valid and legally binding
                 obligations of the Company, entitled to the benefits of the
                 Indenture, and enforceable against the Company in accordance
                 with their terms, except that the enforcement thereof may be
                 subject to (i) bankruptcy, insolvency, reorganization,
                 fraudulent conveyance, moratorium or other similar laws now or
                 hereafter in effect relating to creditors' rights generally
                 and (ii) general principles of equity and the discretion of
                 the court before which any proceeding therefor may be brought
                 (regardless of whether such enforcement is considered in a
                 proceeding in equity or at law).

                                 (vii)  The Exchange Notes and the Private
                 Exchange Notes have been duly and validly authorized by the
                 Company.  When the Exchange Notes and the Private Exchange
                 Notes have been duly executed and delivered by the Company in
                 accordance with the terms of the Registration Rights Agreement
                 and the Indenture (assuming the due authorization, execution
                 and delivery of the Indenture by the Trustee and due
                 authentication and delivery of the Exchange Notes and the
                 Private Exchange Notes by the Trustee in accordance with the
                 Indenture), will constitute the valid and legally binding
                 obligations of the Company, entitled to the benefits of the
                 Indenture, and enforceable against the Company, in accordance
                 with their terms, except that the enforcement thereof may be
                 subject to (i) bankruptcy, insolvency, reorganization,
                 fraudulent conveyance, moratorium or other similar laws now or
                 hereafter in effect relating to creditors' rights generally
                 and (ii) general principles of equity and the discretion of
                 the court before which any proceeding therefor may be brought
                 (regardless of whether such enforcement is considered in a
                 proceeding in equity or at law).

                                (viii)  The  Company has all requisite
                 corporate power and authority to execute, deliver and perform
                 its obligations under the Registration Rights Agreement; the
                 Registration Rights Agreement has been duly and validly
                 authorized, executed and delivered by the Company.  The
                 Registration Rights Agreement (assuming due authorization,
                 execution and delivery thereof by the Initial Purchasers)
                 constitutes the valid and legally binding agreement of the
                 Company enforceable against the Company in accordance with its
                 terms, except that (A) the enforcement thereof may be subject
                 to (i) bankruptcy, insolvency, reorganization, fraudulent
                 conveyance, moratorium or other similar laws now or hereafter
                 in effect relating to





                                       15
<PAGE>   16
                 creditors' rights generally and (ii) general principles of
                 equity and the discretion of the court before which any
                 proceeding therefor may be brought (regardless of whether such
                 enforcement is considered in a proceeding in equity or at law)
                 and (B) any rights to indemnity or contribution thereunder may
                 be limited by federal and state securities laws and public
                 policy considerations.

                                  (ix)  Each of the Indenture, the Securities,
                 the Exchange Notes, the Private Exchange Notes and the
                 Registration Rights Agreement conforms as to legal matters in
                 all material respects to the descriptions thereof contained in
                 the Final Memorandum.

                                   (x)  No legal or governmental proceedings
                 are pending or, to the knowledge of such counsel, threatened
                 to which the Company or any Subsidiary is a party or to which
                 the property or assets of the Company or any Subsidiary is
                 subject which would be required under the Act to be described
                 in a registration statement or in a prospectus and are not
                 described in the Final Memorandum, or which seek to restrain,
                 enjoin, prevent the consummation of or otherwise challenge the
                 issuance or sale of the Securities to be sold hereunder or the
                 consummation of the other transactions described in the Final
                 Memorandum.

                                  (xi)  To the knowledge of such counsel, no
                 contract, agreement or other document to which the Company or
                 any Subsidiary is a party would be required under the Act to
                 be described in a registration statement or prospectus that is
                 not described in the Final Memorandum.

                                 (xii)  The statements in the Final Memorandum,
                 insofar as they are descriptions of contracts, agreements or
                 other legal documents, or refer to statements of law or legal
                 conclusions, are accurate and present fairly the information
                 described therein.

                                (xiii)  Neither the Company nor any Subsidiary
                 is (i) in violation of its certificate of incorporation or
                 bylaws, (ii) in breach or violation of any statute, judgment,
                 decree, order, rule or regulation applicable to it or any of
                 its properties or assets and known to such counsel, except for
                 any such breach or violation which would not, individually or
                 in the aggregate, have a Material Adverse Effect, or (iii) to
                 the knowledge of such counsel, in breach or default under (nor
                 has any event occurred which, with notice or passage of time
                 or both, would constitute a default under) or in violation of
                 any of the terms or provisions of any Contracts known to such
                 counsel, except for any such breach, default, violation or
                 event which would not, individually or in the aggregate, have
                 a Material Adverse Effect.

                                 (xiv)  The execution, delivery and performance
                 of this Agreement, the Indenture, the Registration Rights
                 Agreement, and the consummation of the





                                       16
<PAGE>   17
                 transactions contemplated hereby and thereby (including,
                 without limitation, the issuance and sale of the Securities to
                 the Initial Purchasers) will not conflict with or constitute
                 or result in a breach or a default under (or an event which
                 with notice or passage of time or both would constitute a
                 default under) or violation of or cause an acceleration of any
                 obligation under, or result in the imposition or creation of
                 (or the obligation to create or impose) a lien on any property
                 or assets of the Company or any Subsidiary with respect to (i)
                 the terms or provisions of any Contract known to such counsel,
                 (ii) the certificate of incorporation or bylaws of the Company
                 or any Subsidiary, or (iii) (assuming compliance with all
                 applicable state securities or "Blue Sky" laws and assuming
                 the accuracy of the representations and warranties of the
                 Initial Purchasers in Section 8 hereof) any statute, judgment,
                 decree, order, rule or regulation applicable to the Company or
                 any Subsidiary and known to such counsel and applicable to
                 transactions of the type contemplated by the Final Memorandum.

                                  (xv)  No consent, approval, authorization or
                 order of any governmental authority is required for the
                 issuance and sale by the Company of the Securities to the
                 Initial Purchasers or the other transactions contemplated in
                 this Agreement, except such as may be required under Blue Sky
                 laws, as to which such counsel need express no opinion, and
                 those which have previously been obtained.

                                 (xvi)  To the knowledge of such counsel, the
                 Company and the Subsidiaries have obtained all Permits
                 necessary to conduct the businesses now or proposed to be
                 conducted by them as described in the Final Memorandum, the
                 lack of which would, individually or in the aggregate, have a
                 Material Adverse Effect; each of the Company and the
                 Subsidiaries has fulfilled and performed all of its
                 obligations with respect to such Permits and no event has
                 occurred which allows, or after notice or lapse of time would
                 allow, revocation or termination thereof or results in any
                 other material impairment of the rights of the holder of any
                 such Permit, except for any such revocation or termination
                 which would not have a Material Adverse Effect.

                                (xvii)  None of the Company or the Subsidiaries
                 is, or immediately after the sale of the Securities to be sold
                 hereunder and the application of the proceeds from such sale
                 (as described in the Final Memorandum under the caption "Use
                 of Proceeds") will be, an "investment company" as such term is
                 defined in the Investment Company Act of 1940, as amended.

                               (xviii)  No registration under the Act of the
                 Securities is required in connection with the sale of the
                 Securities to the Initial Purchasers as contemplated by this
                 Agreement and the Final Memorandum or in connection with the
                 initial resale of the Securities by the Initial Purchasers in
                 accordance with Section 8 of this Agreement, in each case
                 assuming (i) that the purchasers who buy such Securities in
                 the initial resale thereof are qualified institutional buyers
                 as defined in Rule 144A





                                       17
<PAGE>   18
                 promulgated under the Act ("QIBs") or, in the case of offers
                 outside of the United States, persons other than U.S. persons,
                 (ii) the accuracy of the Initial Purchasers' representations
                 in Section 8 and those of the Company contained in this
                 Agreement regarding the absence of a general solicitation in
                 connection with the sale of such Securities to the Initial
                 Purchasers and the initial resale thereof, and (iii) the due
                 performance by the Initial Purchasers of the agreements set
                 forth in Section 8 hereof.

                                 (xix)  Neither the consummation of the
                 transactions contemplated by this Agreement nor the sale,
                 issuance, execution or delivery of the Securities will violate
                 Regulation G, T, U or X of the Board of Governors of the
                 Federal Reserve System.

                 At the time the foregoing opinion is delivered, such counsel
         shall additionally state that it has participated in conferences with
         officers and other representatives of the Company, representatives of
         the independent public accountants for the Company, representatives of
         the Initial Purchasers and counsel for the Initial Purchasers, at
         which conferences the contents of the Final Memorandum and related
         matters were discussed, and, although it has not independently
         verified and is not passing upon and assumes no responsibility for the
         accuracy, completeness or fairness of the statements contained in the
         Final Memorandum (except to the extent specified in subsection
         7(a)(ix) and (xii)), no facts have come to its attention which lead it
         to believe that the Final Memorandum, on the date thereof or at the
         Closing Date, contained an untrue statement of a material fact or
         omitted to state a material fact required to be stated therein or
         necessary to make the statements contained therein, in the light of
         the circumstances under which they were made, not misleading (it being
         understood that such firm need express no opinion with respect to the
         financial statements and related notes thereto and the other
         financial, statistical, accounting, reserve and well data included in
         the Final Memorandum).  The opinion of such counsel  described in this
         Section shall be rendered to the Initial Purchasers at the request of
         the Company and shall so state therein.

                 References to the Final Memorandum in this subsection (a)
         shall include any amendment or supplement thereto prepared in
         accordance with the provisions of this Agreement at the Closing Date.

                 In rendering such opinion, such counsel may state that they
         express no opinion as to the laws of any jurisdiction other than the
         federal laws of the United States, the laws of the State of Texas and
         the General Corporation Law of the State of Delaware.  Such counsel
         may also state that, insofar as such opinion involves factual matters,
         such counsel have relied, to the extent they deem proper, upon
         certificates of officers of the Company and certificates of public
         officials; provided that such certificates have been provided to the
         Initial Purchasers.

                 (b)      The Initial Purchasers shall have received an
         opinion, dated the Closing Date, of Cahill Gordon & Reindel, counsel
         for the Initial Purchasers, with respect to certain legal





                                       18
<PAGE>   19
         matters relating to this Agreement, and such other related matters as
         the Initial Purchasers may reasonably require.  In rendering such
         opinion, Cahill Gordon & Reindel shall have received and may rely upon
         such certificates and other documents and information as they may
         reasonably request to pass upon such matters.

                 (c)      The Initial Purchasers shall have received from KPMG
         Peat Marwick LLP, independent public accountants for the Company,
         comfort letters, dated the date hereof and the Closing Date, in form
         and substance reasonably satisfactory to the Initial Purchasers and
         counsel for the Initial Purchasers.

                 (d)      The representations and warranties of the Company
         contained in this Agreement shall be true and correct in all material
         respects on and as of the Closing Date as if made on and as of the
         Closing Date; each of the Company shall  have performed all covenants
         and agreements and satisfied all conditions on its part to be
         performed or satisfied hereunder at or prior to the Closing Date; and,
         except as set forth in the Final Memorandum (exclusive of any
         amendment or supplement thereto after the date hereof) subsequent to
         the date of the most recent financial statements in such Final
         Memorandum, there shall have been no event or development that,
         individually or in the aggregate, has or would be reasonably likely to
         have a Material Adverse Effect.

                 (e)      The issuance and sale of the Securities pursuant to
         this Agreement shall not be enjoined (temporarily or permanently) and
         no restraining order or other injunctive order shall have been issued
         or any action, suit or proceeding shall have been commenced with
         respect to this Agreement before any court or governmental authority.

                 (f)      The Initial Purchasers shall have received
         certificates, dated the Closing Date, signed on behalf of the Company
         by its Chief Executive Officer and Chief Financial Officer to the
         effect that:

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

                          (ii)    At the Closing Date, since the date hereof or
                 since the date of the most recent financial statements in the
                 Final Memorandum (exclusive of any amendment or supplement
                 thereto after the date hereof), no event or events have
                 occurred, no information has become known nor does any
                 condition exist that, individually or in the aggregate, would
                 have a Material Adverse Effect; and

                          (iii)   The sale of the Securities hereunder has not
                 been enjoined (temporarily or permanently).





                                       19
<PAGE>   20
                 (g)      On the Closing Date, the Initial Purchasers shall
         have received the Registration Rights Agreement executed by the
         Company and such agreement shall be in full force and effect at all
         times from and after the Closing Date.

                 (h)      On or before the Closing Date, the Initial Purchasers
         and counsel for the Initial Purchasers shall have received such
         further documents, certificates and schedules or instruments relating
         to the business, corporate, legal and financial affairs of the Company
         as they shall have heretofore reasonably requested from the Company.

         All such documents, opinions, certificates and schedules or
instruments delivered pursuant to this Agreement will comply with the
provisions hereof only if they are reasonably satisfactory in all material
respects to the Initial Purchasers and counsel for the Initial Purchasers.  The
Company shall furnish to the Initial Purchasers such conformed copies of such
documents, opinions, certificates and schedules or instruments in such
quantities as the Initial Purchasers shall reasonably request.

         8.      Offering of Securities; Restrictions on Transfer.  Each of the
Initial Purchasers represents and warrants (as to itself only) that it is a
QIB.  Each of the Initial Purchasers agrees with the Company (as to itself
only) that (i) it has not and will not solicit offers for, or offer or sell,
the Securities by any form of general solicitation or general advertising (as
those terms are used in Regulation D under the Act) or in any manner involving
a public offering within the meaning of Section 4(2) of the Act; and (ii) it
has and will solicit offers for the Securities only from, and will offer the
Securities only to (A) in the case of offers inside the United States, persons
whom the Initial Purchasers reasonably believe to be QIBs or, if any such
person is buying for one or more institutional accounts for which such person
is acting as fiduciary or agent, only when such person has represented to the
Initial Purchasers that each such account is a QIB, to whom notice has been
given that such sale or delivery is being made in reliance on Rule 144A, and,
in each case, in transactions under Rule 144A and (B) in the case of offers
outside the United States, to persons other than U.S. persons ("foreign
purchasers," which term shall include dealers or other professional fiduciaries
in the United States acting on a discretionary basis for foreign beneficial
owners (other than an estate or trust)).

         9.      Indemnification and Contribution.  (a)  The Company agrees to
indemnify and hold harmless the Initial Purchasers and the affiliates,
directors, officers, agents, representatives and employees of the Initial
Purchasers, and each other person, if any, who controls any Initial Purchaser
within the meaning of Section 15 of the Act or Section 20 of the Exchange Act,
against any losses, claims, damages or liabilities, joint or several, to which
any Initial Purchaser or any such affiliate, director, officer, agent,
representative, employee or controlling person may become subject under the
Act, the Exchange Act or otherwise, insofar as any such losses, claims, damages
or liabilities (or actions in respect thereof) arise out of or are based upon:

                          (i)     any untrue statement or alleged untrue
                 statement of any material fact contained in (A) any Memorandum
                 or any amendment or supplement thereto or (B)





                                       20
<PAGE>   21
                 any application or other document, or any amendment or
                 supplement thereto, executed by the Company or based upon
                 written information furnished by or on behalf of the Company
                 filed in any jurisdiction in order to qualify the Securities
                 under the securities or "Blue Sky" laws thereof or filed with
                 any securities association or securities exchange (each, an
                 "Application"); or

                          (ii)    the omission or alleged omission to state, in
                 any Memorandum or any amendment or supplement thereto, or any
                 Application, a 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,

and will reimburse, as incurred, the Initial Purchasers and each such
affiliate, director, officer, agent, representative and employee and each such
controlling person for any legal or other expenses reasonably incurred by the
Initial Purchasers, such affiliate, director, officer, agent, representative or
employee or such  controlling person in connection with investigating,
defending against or appearing as a third-party witness in connection with any
such loss, claim, damage, liability or action; provided, however, that the
Company will not be liable (i) in any such case to the extent that any such
loss, claim, damage, or liability arises out of or is based upon any untrue
statement or alleged untrue statement or omission or alleged omission made in
any Memorandum or any amendment or supplement thereto, or any Application, in
reliance upon and in conformity with written information furnished to the
Company by the Initial Purchasers specifically for use therein or (ii) with
respect to the Preliminary Memorandum, to the extent that any such loss, claim,
damage or liability arises solely from the fact that the Initial Purchasers
sold Securities to a person to whom there was not sent or given a copy of the
Final Memorandum (as amended or supplemented) at or prior to the written
confirmation of such sale if the Company shall have previously furnished copies
thereof to the Initial Purchasers in accordance with Section 5(d) hereof and
the Final Memorandum (as amended or supplemented) would have corrected any such
untrue statement or omission.  This indemnity agreement will be in addition to
any liability that the Company may otherwise have to the indemnified parties.
The Company shall not be liable under this paragraph (a) for any settlement of
any claim or action effected without their consent, which consent shall not be
unreasonably withheld or delayed.

         The Initial Purchasers shall not, without the prior written consent of
the Company, effect any settlement or compromise of any pending or threatened
proceeding in respect of which the Company is or could have been a party, or
indemnity could have been sought hereunder by the Company, unless such
settlement (A) includes an unconditional written release of the Company, in
form and substance reasonably satisfactory to the Company, from all liability
on claims that are the subject matter of such proceeding and (B) does not
include any statement as to an admission of fault, culpability or failure to
act by or on behalf of the Company.

                 (b)      The Initial Purchasers agree, severally and not
         jointly, to indemnify and hold harmless the Company, its affiliates,
         directors, officers, agents, representatives and employees and each
         other person, if any, who controls the Company within the meaning of





                                       21
<PAGE>   22
         Section 15 of the Act or Section 20 of the Exchange Act against any
         losses, claims, damages or liabilities to which the Company or any
         such affiliate, director, officer, agent, representative, employees or
         controlling person may become subject under the Act, the Exchange Act
         or otherwise, insofar as such losses, claims, damages or liabilities
         (or actions in respect thereof) arise out of or are based upon (i) any
         untrue statement or alleged untrue statement of any material fact
         contained in any Memorandum or any amendments or supplement thereto,
         or any Application or (ii) the omission or the alleged omission to
         state therein a material fact required to be stated in any Memorandum
         or any amendment or supplement thereto, or any Application, or
         necessary to make the statements therein not misleading, in each case
         to the extent, but only to the extent, that such untrue statement or
         alleged untrue statement or omission or alleged omission was made in
         reliance upon and in conformity with written information concerning
         such Initial Purchaser furnished to the Company by such Initial
         Purchaser specifically for use therein; and, subject to the limitation
         set forth immediately preceding this clause, will reimburse, as
         incurred, any legal or other expenses reasonably incurred by the
         Company or any such affiliate, director, officer, agent,
         representative,  employee or controlling person in connection with
         investigating or defending against or appearing as a third party
         witness in connection with any such loss, claim, damage, liability or
         action in respect thereof.  This indemnity agreement will be in
         addition to any liability that the Initial Purchasers may otherwise
         have to the indemnified parties.  The Initial Purchasers shall not be
         liable under this Section 9 for any settlement of any claim or action
         effected without their consent, which consent shall not be
         unreasonably withheld or delayed.


         The Company shall not, without the prior written consent of the
Initial Purchasers, effect any settlement or compromise of any pending or
threatened proceeding in respect of which any Initial Purchaser is or could
have been a party, or indemnity could have been sought hereunder by any Initial
Purchaser, unless such settlement (A) includes an unconditional written release
of the Initial Purchasers, in form and substance reasonably satisfactory to the
Initial Purchasers, from all liability on claims that are the subject matter of
such proceeding and (B) does not include any statement as to an admission of
fault, culpability or failure to act by or on behalf of any Initial Purchaser.

                 (c)      Promptly after receipt by an indemnified party under
         this Section 9 of notice of the commencement of any action for which
         such indemnified party is entitled to indemnification under this
         Section 9, such indemnified party will, if a claim in respect thereof
         is to be made against the indemnifying party under this Section 9,
         notify the indemnifying party of the commencement thereof in writing;
         but the omission to so notify the indemnifying party (i) will not
         relieve it from any liability under paragraph (a) or (b) above unless
         and to the extent 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 paragraphs (a) and (b) above.  In case any such action is
         brought against any indemnified party, and it notifies the
         indemnifying party of the commencement thereof, the indemnifying party
         will be entitled to participate therein and, to the extent that it may
         wish,





                                       22
<PAGE>   23
         jointly with any other  indemnifying party similarly notified, to
         assume the defense thereof, with counsel reasonably satisfactory to
         such indemnified party; provided, however, that 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
         defendants in any such action include both the indemnified party and
         the indemnifying party and the indemnified party shall have been
         advised by counsel that there may be one or more legal defenses
         available to it and/or other indemnified parties that are different
         from or additional to those available to the indemnifying party, or
         (iii) the indemnifying party shall not have employed counsel
         reasonably satisfactory to the indemnified party to represent the
         indemnified party within a reasonable time after receipt by the
         indemnifying party of notice of the institution of such action, then,
         in each such case, the indemnifying party shall not have the right to
         direct the defense of such action on behalf of such indemnified party
         or parties and such indemnified party or parties shall have the right
         to select separate counsel to defend such action on behalf of such
         indemnified party or parties.  After notice from the indemnifying
         party to such indemnified party of its election so to assume the
         defense thereof and approval by such indemnified party of counsel
         appointed to defend such action, the indemnifying party will not be
         liable to such indemnified party under this Section 9 for any legal or
         other expenses, other than reasonable costs of investigation,
         subsequently incurred by such indemnified party in connection with the
         defense thereof, unless (i) the indemnified party shall have employed
         separate counsel in accordance with the proviso to the immediately
         preceding sentence (it being understood, however, that in connection
         with such action the indemnifying party shall not be liable for the
         expenses of more than one separate counsel (in addition to local
         counsel) in any one action or separate but substantially similar
         actions in the same jurisdiction arising out of the same general
         allegations or circumstances, designated by BT Alex. Brown
         Incorporated in the case of paragraph (a) of this Section 9 or the
         Company in the case of paragraph (b) of this Section 9, representing
         the indemnified parties under such paragraph (a) or paragraph (b), as
         the case may be, who are parties to such action or actions) or (ii)
         the indemnifying party has authorized in writing the employment of
         counsel for the indemnified party at the expense of the indemnifying
         party.  After such notice from the indemnifying party to such
         indemnified party, the indemnifying party will not be liable for the
         costs and expenses of any settlement of such action effected by such
         indemnified party without the prior written consent of the
         indemnifying party (which consent shall not be unreasonably withheld),
         unless such indemnified party waived in writing its rights under this
         Section 9, in which case the indemnified party may effect such a
         settlement without such consent.

                 (d)      In circumstances in which the indemnity agreement
         provided for in the preceding paragraphs of this Section 9 is
         unavailable to, or insufficient to hold harmless, an indemnified party
         in respect of any losses, claims, damages or liabilities (or actions
         in respect thereof), each indemnifying party, in order to provide for
         just and equitable contribution, shall contribute to the amount paid
         or payable by such indemnified party as a result of such losses,
         claims, damages or liabilities (or actions in respect thereof) in such
         proportion as is appropriate to reflect (i) the relative benefits
         received by the indemnifying party or parties on the one hand and the
         indemnified party on the other from the offering of the Securities





                                       23
<PAGE>   24
         or (ii) if the allocation provided by the foregoing clause (i) is not
         permitted by applicable law, not only such relative benefits but also
         the relative fault of the indemnifying party or parties on the one
         hand and the indemnified party on the other in connection with the
         statements or omissions or alleged statements or omissions that
         resulted in such losses, claims, damages or liabilities (or actions in
         respect thereof).  The relative benefits received by the Company on
         the one hand and any Initial Purchaser on the other shall be deemed to
         be in the same proportion as the total proceeds from the offering
         (before deducting expenses) received by the Company bear to the total
         discounts and commissions received by such Initial Purchaser.  The
         relative fault of the parties shall be determined by reference to,
         among other things, whether the untrue or alleged untrue statement of
         a material fact or the omission or alleged omission to state a
         material fact relates to information supplied by the Company on the
         one hand, or such Initial Purchaser on the other, the parties'
         relative intent, knowledge, access to information and opportunity to
         correct or prevent such statement or omission or alleged statement or
         omission, and any other equitable considerations appropriate in the
         circumstances.  The Company and the Initial Purchasers agree that it
         would not be just and equitable if the amount of such contribution
         were determined by pro rata or per capita allocation or by any other
         method of allocation that does not take into account the equitable
         considerations referred to in the first sentence of this paragraph
         (d).  Notwithstanding any other provision of this paragraph (d), no
         Initial Purchaser shall be obligated to make contributions hereunder
         that in the aggregate exceed the total discounts, commissions and
         other compensation received by such  Initial Purchaser under this
         Agreement, less the aggregate amount of any damages that such Initial
         Purchaser has otherwise been required to pay by reason of the untrue
         or alleged untrue statements or the omissions or alleged omissions to
         state a material fact, and no person guilty of fraudulent
         misrepresentation (within the meaning of Section 11(f) of the Act)
         shall be entitled to contribution from any person who was not guilty
         of such fraudulent misrepresentation.  For purposes of this paragraph
         (d), each affiliate, director, officer, agent, representative and
         employee of an Initial Purchaser and each person, if any, who controls
         an Initial Purchaser within the meaning of Section 15 of the Act or
         Section 20 of the Exchange Act shall have the same rights to
         contribution as the Initial Purchasers, and each director and officer
         of the Company and each person, if any, who controls the Company
         within the meaning of Section 15 of the Act or Section 20 of the
         Exchange Act, shall have the same rights to contribution as the
         Company.

         10.     Survival Clause.  The respective representations, warranties,
agreements, covenants, indemnities and other statements of the Company, its
officers and the Initial Purchasers set forth in this Agreement or made by or
on behalf of them, respectively, pursuant to this Agreement shall remain in
full force and effect, regardless of (i) any investigation made by or on behalf
of the Company, any of its  officers or directors, the Initial Purchasers or
any controlling person referred to in Section 9 hereof and (ii) delivery of and
payment for the Securities.  The respective agreements, covenants, indemnities
and other statements set forth in Sections 6, 9 and 15 hereof shall remain in
full force and effect, regardless of any termination or cancellation of this
Agreement.





                                       24
<PAGE>   25
         11.     Termination.  (a)  This Agreement may be terminated in the
sole discretion of the Initial Purchasers by notice to the Company given prior
to the Closing Date in the event that the Company shall have failed, refused or
been unable to perform, in all material respects, all obligations and satisfy
all conditions on its part to be performed or satisfied hereunder at or prior
thereto or, if at or prior to the Closing Date:


                     (i) either (i) the Company shall have sustained any loss
         or interference with respect to its businesses or properties from
         fire, flood, hurricane, accident or other calamity, whether or not
         covered by insurance, or from any strike, labor dispute, slow down or
         work stoppage or any legal or governmental proceeding, which loss or
         interference, in the sole judgment of the Initial Purchasers, has had
         or has a Material Adverse Effect, or (ii) there shall have been, in
         the sole judgment of the Initial Purchasers, any event or development
         that, individually or in the aggregate, has or could be reasonably
         likely to have a Material Adverse Effect (including without limitation
         a change in control of the Company), except in each case as described
         in the Final Memorandum (exclusive of any amendment or supplement
         thereto);

                    (ii) trading in securities generally on the New York Stock
         Exchange, the American Stock Exchange or the NASDAQ National Market
         shall have been suspended or maximum or minimum prices shall have been
         established on any such exchange or market;

                   (iii) a banking moratorium shall have been declared by New
         York or United States authorities;

                    (iv) there shall have been (A) an outbreak or escalation of
         hostilities between the United States and any foreign power, or (B) an
         outbreak or escalation of any other insurrection or armed conflict
         involving the United States or any other national or international
         calamity or emergency or (C) any material change in the financial
         markets of the United States that, in the case of (A), (B) or (C)
         above and in the sole judgment of the Initial Purchasers, makes it
         impracticable or inadvisable to proceed with the offering or the
         delivery of the Securities as contemplated by the Final Memorandum; or

                     (v) any securities of the Company shall have been
         downgraded or placed on any "watch list" for possible downgrading by
         any nationally recognized statistical rating organization.

                 (b)      Termination of this Agreement pursuant to this
         Section 11 shall be without liability of any party to any other party
         except as provided in Section 10 hereof.

         12.     Information Supplied by the Initial Purchasers.  The
statements set forth in the legend on the inside front cover concerning
over-allotment and trading activities by the Initial Purchasers, the last
paragraph of the cover page and the third and seventh paragraphs of the section
entitled





                                       25
<PAGE>   26
"Private Placement" constitute the only information furnished by the Initial
Purchasers to the Company for the purposes of Sections 2(a) and 9 hereof.

         13.     Notices.  All communications hereunder shall be in writing
and, if sent to the Initial Purchasers, shall be mailed or delivered or
telecopied and confirmed in writing to BT Alex. Brown Incorporated, One Bankers
Trust Plaza, 130 Liberty Street, New York, New York 10006, Attention:
Corporate Finance Department, and if sent to the Company, shall be mailed,
delivered or telecopied and confirmed in writing to the Company at Costilla
Energy, Inc., 400 West Illinois, Suite 1000, Midland, Texas 79701 Attention:
Chief Financial Officer.

         14.     Successors.  This Agreement shall inure to the benefit of and
be binding upon the Initial Purchasers, the Company and their respective
successors, assigns and legal representatives, and nothing expressed or
mentioned in this Agreement is intended or shall be construed to give any other
person any legal or equitable right, remedy or claim under or in respect of
this Agreement, or any provisions herein contained; this Agreement and all
conditions and provisions hereof being intended to be and being for the sole
and exclusive benefit of the Initial Purchasers, the Company and their
respective successors, assigns and legal representatives and for the benefit of
no other person except that (i) the indemnities of the Company contained in
Section 9 of this Agreement shall also be for the benefit of the affiliates,
directors, officers, agents, representatives and employees of the Initial
Purchasers and any person or persons who control any of the Initial Purchasers
within the meaning of Section 15 of the Act or Section 20 of the Exchange Act
and (ii) the indemnities of the Initial Purchasers contained in Section 9 of
this Agreement shall also be for the benefit of the affiliates, directors,
officers, agents, representatives and employees of the Company and any person
or persons who control the Company within the meaning of Section 15 of the Act
or Section 20 of the Exchange Act.  No purchaser of any of the Securities from
the Initial Purchasers will be deemed a successor because of such purchase.

         15.     APPLICABLE LAW.  THE VALIDITY AND INTERPRETATION OF THIS
AGREEMENT, AND THE TERMS AND CONDITIONS SET FORTH HEREIN SHALL BE GOVERNED BY
AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT
GIVING EFFECT TO ANY PROVISIONS RELATING TO CONFLICTS OF LAW.

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





                                       26
<PAGE>   27
                                      S-1


         If the foregoing correctly sets forth our understanding, please
indicate your acceptance thereof in the space provided below for that purpose,
whereupon this letter shall constitute a binding agreement among the Company
and the Initial Purchasers.

                                       Very truly yours,
                                  
                                       COSTILLA ENERGY, INC.
                                  
                                  
                                       By:    /s/ Bobby W. Page
                                             ----------------------------------
                                             Name:  Bobby W. Page
                                             Title: Senior Vice President





                                       1
<PAGE>   28
                                      S-2


The foregoing Agreement is hereby confirmed and accepted as of the date first
above written.

BT ALEX. BROWN INCORPORATED


By:  /s/ Richard J. Doleshek                                            
    --------------------------------
     Name: Richard J. Doleshek
     Title: Managing Director

PRUDENTIAL SECURITIES INCORPORATED


By:  /s/ Peter Horan                                                         
    --------------------------------
     Name: Peter Horan
     Title: Managing Director





                                       2
<PAGE>   29
                                   SCHEDULE I

<TABLE>
<CAPTION>
                                                                    Principal Amount of
Initial Purchaser                                                   Securities To Be Purchased
-----------------                                                   --------------------------
<S>                                                                        <C>

BT Alex. Brown Incorporated   . . . . . . . . . . . . . . . . .            $ 60,000,000

Prudential Securities Incorporated    . . . . . . . . . . . . .              20,000,000
                                                                             ----------

                                  Total   . . . . . . . . . . .            $ 80,000,000
                                                                             ==========
</TABLE>





                                       3