<PAGE>   1
                                                                   EXHIBIT 10.25

                              SECOND AMENDMENT TO
                     AMENDED AND RESTATED CREDIT AGREEMENT

                 This Second Amendment to Amended and Restated Credit Agreement
(this "Amendment") dated as of January 14, 1998 is among COSTILLA ENERGY, INC.,
a Delaware corporation (the "Borrower"), the banks named on the signature pages
hereto (together with their respective successors and assigns in such capacity,
the "Banks"), BANKERS TRUST COMPANY, as agent for the Banks (together with its
successors and assigns in such capacity, the "Agent") and UNION BANK OF
CALIFORNIA, N.A., as co-agent for the Banks (together with its successors and
assigns in such capacity, the ("Co-Agent").

                             PRELIMINARY STATEMENT

                 A.       The Borrower and the Bank Group have entered into
that certain Amended and Restated Credit Agreement dated as of August 28, 1997
as amended by that certain First Amendment to Amended and Restated Credit
Agreement dated as of December 30, 1997 (as so amended, the "Credit
Agreement").

                 B.       The Borrower and the Bank Group desire to further
amend the Credit Agreement as set forth herein.

                 NOW THEREFORE, in consideration of the foregoing and the
mutual agreements set forth herein, the parties agree as follows:

                 Section 1. Definitions. Unless otherwise defined in this 
Amendment, each capitalized term used in this Amendment has the meaning 
assigned to such term in the Credit Agreement.

                 Section 2. Amendments. The Credit Agreement is hereby amended
as follows:

                 a.       The second sentence of Section 2.04(a) of the Credit
         Agreement is hereby amended in its entirety to read as follows:

                          "During the period from and after January 14, 1998
                 until the Borrowing Base is redetermined in accordance with
                 this Section, the amount of the Borrowing Base shall be
                 $36,500,000; provided, however, that if the Borrower acquires
                 the Manti Properties prior to the date that all outstanding
                 "Obligations" under the Acquisition Credit Agreement are
                 repaid in full the amount of the Borrowing Base shall be
                 automatically increased to $45,000,000 during the period from
                 the date of such acquisition until the Borrowing Base is
                 redetermined in accordance with this Section; and provided
                 further that if all outstanding "Obligations" under the
                 Acquisition Credit Agreement are repaid in full (regardless of
                 whether the Borrower has acquired the Manti Properties) the
                 amount of the Borrowing Base shall be automatically increased
                 to $50,000,000 during the period from the date of such
                 repayment until the Borrowing Base is redetermined in
                 accordance with this Section."
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                 b.       Section 6.01 of the Credit Agreement is hereby
         amended by adding the following subclause (g) immediately prior to the
         period at the end of Section 6.01:

                          "; and (g) Indebtedness of Costilla Pipeline owing to
                 the Borrower in respect of the loan by the Borrower to
                 Costilla Pipeline permitted under Section 6.09(g)"

                 c.       Section 6.09 of the Credit Agreement is hereby
         amended by adding the following subclause (g) immediately prior to the
         period at the end of Section 6.09:

                          ", and (g) capital contributions and loans by the
                 Borrower to Costilla Pipeline in an aggregate amount not to
                 exceed $1,800,000 to acquire and operate a gas gathering
                 system in Pecos County, Texas acquired from W. Wilson Corp."

                 d.       Section 6.10 of the Credit Agreement is hereby
         amended in its entirety to read as follows:

                          "Section 6.10 Lines of Business. The Borrower will
                 not, and will not permit any of its Subsidiaries to, directly
                 or indirectly engage in any business other than the
                 acquisition, disposition, exploration, ownership, development
                 and operation of Oil and Gas Properties and the acquisition,
                 disposition, ownership and operation of gas gathering,
                 transportation and processing systems related to such Oil and
                 Gas Properties, which ownership and operation of gas
                 gathering, transportation and processing systems may include
                 the gathering, transportation and/or processing of gas owned
                 by third parties."

                 e.       The definitions of "Indenture" and "Senior Unsecured
         Notes" in Annex A of the Credit Agreement are hereby amended in their
         entirety to read as follows:

                          ""Indenture" means that certain Indenture, dated as of
                 October 1, 1996, by and between the Borrower as issuer and
                 State Street Bank & Trust Company as trustee, as amended by
                 the Supplemental Indenture to be dated on or about January 16,
                 1998, pursuant to which the Borrower issued the Senior
                 Unsecured Notes."

                          ""Senior Unsecured Notes" means the $180,000,000 of
                 10.25% Senior Unsecured Notes due 2006 issued under the
                 Indenture."

                 f.       The following defined terms are hereby added to Annex
         A of the Credit Agreement in their appropriate alphabetical order:

                          ""Costilla Pipeline" means Costilla Energy Pipeline
                 Corporation, a Texas corporation and wholly-owned Subsidiary
                 of the Borrower."




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                          "Manti Acquisition Documents" means, collectively,
                 the Purchase and Sale Agreement dated December 2, 1997, between
                 Manti Resources, Inc., et al. and the Borrower, and all
                 assignments, documents, agreements and instruments executed
                 thereunder or in connection therewith."

                          "Manti Properties" means the Oil and Gas Properties
                 and related assets situated in Brooks County, Texas to be
                 acquired by the Borrower under the Manti Acquisition
                 Documents."

                 g.       Schedule 4.01 of the Credit Agreement is hereby
         amended in its entirety to read as Schedule 4.01 attached hereto.

                 Section 3. Acquisition Credit Agreement. The Borrower shall use
a portion of the proceeds from the Senior Unsecured Notes issued after the date
hereof to repay all outstanding "Obligations" under the Acquisition Credit
Agreement. Upon such repayment all references in the Credit Agreement to the
Acquisition Credit Agreement and the Acquisition Loan Documents shall be deemed
deleted or no longer applicable, as appropriate.

                 Section 4. Manti  Acquisition. Immediately following the
acquisition of the Manti Properties by the Borrower, the Borrower shall deliver
to the Agent the following documents: (a) a fully executed and acknowledged
counterpart of the assignment of the Manti Properties from Manti Resources,
Inc., et al. to the Borrower; and (b) Security Documents, in form and substance
satisfactory to the Agent, executed and acknowledged by the Borrower granting a
first priority lien in favor of the Agent on the Manti Properties.

                 Section 5. Ratification. The Borrower hereby ratifies and
confirms all of the Obligations under the Credit Agreement (as amended hereby)
and the other Loan Documents. All references in the Loan Documents to the
"Credit Agreement" shall mean the Credit Agreement as amended hereby and as the
same may be amended, supplemented, restated or otherwise modified and in effect
from time to time in the future.

                 Section 6. Effectiveness. The effectiveness of this Amendment
is subject to the condition precedent that the Agent shall have received all of
the following, each in form and substance reasonably satisfactory to the Bank
Group and in such number of counterparts as may be reasonably requested by the
Agent:

                 a.       this Amendment executed by the Borrower and each
member of the Bank Group;

                 b.       Security Documents executed by the Borrower pledging
all of the stock of Costilla Pipeline to the Agent together with the
certificate representing such stock and related stock powers executed in blank
by the Borrower;

                 c.       Security Documents executed by the Borrower pledging
the Borrower's equity interest in Costilla Redeco in accordance with Section
5.15 of the Credit Agreement; and

                 d.       a certificate of the secretary or an assistant
secretary of the Borrower certifying, inter alia, (i) true and correct copies
of resolutions adopted by the Board of Directors of the Borrower (A)





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authorizing the execution, delivery and performance by the Borrower of this
Amendment and the other Loan Documents referred to herein, (B) approving the
forms of this Amendment and the other Loan Documents referred to herein, and
(C) authorizing officers of the Borrower to execute and deliver this Amendment
and the other Loan Documents referred to herein, (ii) true and correct copies
of the articles of incorporation and bylaws (or other similar charter
documents) of the Borrower and (iii) the incumbency and specimen signatures of
the officers of the Borrower executing any documents on behalf of it.

                 Section 7. Representations and Warranties. The Borrower hereby
represents and warrants to the Bank Group that (a) the execution, delivery and
performance of this Amendment has been duly authorized by all requisite
corporate action on the part of the Borrower, (b) each of the Credit Agreement
(as amended hereby) and the other Loan Documents to which it is a party
constitutes a valid and legally binding agreement enforceable against the
Borrower in accordance with its terms except, as such enforceability may be
limited by bankruptcy, insolvency, reorganization, moratorium, fraudulent
transfer or other similar laws relating to or affecting the enforcement of
creditors' rights generally and by general principles of equity, (c) the
representations and warranties by the Borrower contained in the Credit
Agreement as amended hereby and in the other Loan Documents are true and
correct on and as of the date hereof in all material respects as though made as
of the date hereof, (d) no Default or Event of Default exists under the Credit
Agreement (as amended hereby) or any of the other Loan Documents.

                 Section 8. Choice of Law. This Amendment shall be governed by,
and construed in accordance with, the laws of the State of New York.

                 Section 9. Final Agreement.  THE CREDIT AGREEMENT (AS AMENDED
HEREBY) AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE
PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR
SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO ORAL AGREEMENTS BETWEEN
THE PARTIES.

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                 IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be executed by its officers thereunto duly authorized as of the
date first above written.

                                        COSTILLA ENERGY, INC.

                                        By:   /s/ BOBBY W. PAGE
                                           ----------------------------------
                                        Name:     Bobby W. Page
                                              -------------------------------
                                        Title:  Senior Vice President
                                              -------------------------------
                                        BANKERS TRUST COMPANY,
                                          as Agent and Bank

                                        By:   /s/ MARY JO JOLLY
                                           ----------------------------------
                                        Name:     Mary Jo Jolly
                                              -------------------------------
                                        Title:  Assistant Vice President
                                              -------------------------------
                                        UNION BANK OF CALIFORNIA, N.A.,
                                          as Co-Agent and Bank

                                        By:   /s/ RANDALL OSTERBER
                                           ----------------------------------
                                        Name:     Randall Osterber
                                              -------------------------------
                                        Title:   Vice President
                                              -------------------------------

                                        By:   /s/ TONY R. WEBER
                                           ----------------------------------
                                        Name:     Tony R. Weber
                                              -------------------------------
                                        Title:  Senior Vice President/Manager
                                              -------------------------------




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                                        DEN NORSKE BANK ASA
                                          as Bank

                                        By:   /s/ MORTEN BJORNSEN
                                           --------------------------------
                                        Name:     Morten Bjornsen
                                             ------------------------------
                                        Title:    Senior Vice President
                                              -----------------------------

                                        By:   /s/ CHARLES E. HALL
                                           --------------------------------
                                        Name:     Charles E. Hall
                                             ------------------------------
                                        Title:    Senior Vice President
                                              -----------------------------

                                        THE TORONTO DOMIMON BANK
                                          as Bank

                                        By:   /s/ JORGE A. GARCIA
                                           --------------------------------
                                        Name:     Jorge A. Garcia
                                             ------------------------------
                                        Title:    Mgr. Cr. Admin.
                                              -----------------------------

                                        WELLS FARGO BANK, N.A.
                                           as Bank

                                        By:   /s/ LESTER J. N. KELIHER
                                           --------------------------------
                                        Name:     Lester J. N. Keliher
                                             ------------------------------
                                        Title:    Vice President
                                              -----------------------------



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                                 SCHEDULE 4.01

                            BORROWER'S SUBSIDIARIES

Costilla Redeco Energy, L.L.C.

Costilla Energy Pipeline Corporation




                                 Schedule 4.01