Migl #3 Encounters 250 Feet of New Sands Below Deepest Producing Zone
                                  in Migl #1
                  Migl #1 Ramps Up Production to 11.5 MMCFD
                        Completion of Migl #2 Underway
            Two New Southwest Speaks Locations Staked for Drilling
   Company Targets Additional Deep Gas With Prices Hedged at $2.40 Per MCF

    MIDLAND, Texas, May 20 /PRNewswire/ -- Costilla Energy, Inc.
(Nasdaq: COSE) announced today that the Migl-Mitchell #3 has encountered over
500 feet of Deep Wilcox sands, including more than 250 feet of new sands below
the deepest producing zone of the Company's highly successful Migl-Mitchell #1
well.  Currently drilling at about 16,500 feet, the Migl #3 is targeting a
total depth of 17,500 feet.  Production is expected to commence in mid-June.
    "This well reinforces the significant potential for Costilla Energy in the
Southwest Speaks project," said Mike Grella, president and CEO of the company.
"In comparison to our Migl-Mitchell #1, which encountered a total of 190 feet
of productive Wilcox sands while drilling to a total depth of 14,950 feet, the
#3 has already logged 500 feet of sands -- at least 250 feet in zones deeper
than we drilled the Migl #1."
    Costilla reported that current daily production from the Migl-Mitchell #1
is up to approximately 11.5 million cubic feet per day (MMCFD) from
approximately 9 MMCFD reported in early May.  Since completion of the Migl #1
in January, it has produced more than 800 MMCF of natural gas.  Reserves in
the Migl #1 are estimated at 25 to 40 billion cubic feet.  Reserve estimates
have not currently been assigned to either the Migl #2 or the Migl #3.
    The Company also reported that the Migl-Mitchell #2, which encountered 274
feet of Deep Wilcox sands in a separate fault block from the Migl #1, is being
completed.  Production from the Migl #2 is expected within a week.
    "The results we are achieving in our Southwest Speaks project continue to
be very rewarding to Costilla," said Grella.  "Our staff has done an
exceptional job of creating significant value from this prospect.  As we drill
and complete these deeper wells, we are conducting extensive tests to assure
we maximize our opportunities in this field as we go forward.  This testing
has caused some delays in bringing on production."
    Grella said that based on seismic analysis and well control data, a
considerable number of additional locations have been identified for future
drilling in the Southwest Speaks project.  The Company has staked locations
for two additional Speaks wells which are planned to commence drilling in
mid-1998.
    Production from the Company's non-operated Cotton Valley reef well, the
McMahon #4, has been temporarily shut in by the operator while a frac job is
being performed.
    As previously announced, Costilla has approximately 100 percent of its gas
production hedged with a floor price of $2.40 per MMBTU, or $2.40 per MCF.
    "With our excellent gas hedging position, our anticipated growth in
production, and our extensive inventory of gas drilling prospects, we are
extremely bullish about Costilla's opportunities in 1998 and beyond," said
Grella.
    Costilla Energy, Inc. is an independent energy company actively engaged in
the exploration, acquisition and development of oil and gas properties, with
operations primarily in the Permian Basin of Texas and New Mexico, South and
East Texas, and the Rocky Mountain regions.  Headquartered in Midland, Texas,
the Company and its predecessors have been in business since 1988.  The
Company's common stock is traded on the Nasdaq National Market under the
symbol COSE.

    Certain statements in this news release constitute "forward-looking
statements" within the meaning of the Private Securities Litigation Reform Act
of 1995.  Such forward-looking statements involve known and unknown risks,
uncertainties, and other factors which may cause the actual results,
performance, or achievements of Costilla Energy, Inc. to be materially
different from any future results, performance, or achievements expressed
or implied by such forward-looking statements.  Such factors include, among
others, the following: the volatility of oil and gas prices; the Company's
ability to replace its oil and gas reserves; the availability of capital
resources; the reliance upon estimates of proved reserves; operating hazards
and uninsured risks; competition; government regulation; and the ability of
the Company to implement its business strategy.  Additional information is
available in the Company's filings with the Securities and Exchange
Commission, which are incorporated by this reference as though fully set forth
herein.

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