Highly Prolific Cotton Valley Reef Drilling Commenced

                    Sale of High Operating Cost Properties

                           Share Buy Back Initiated

    MIDLAND, Texas, June 16 /PRNewswire/ -- Costilla Energy, Inc.
(Nasdaq: COSE), citing a better than 80 percent success rate in wells drilled
so far this year, today announced it is increasing its total 1997 capital
budget by 38 percent to $36 million from $26 million.
    The company has drilled 57 wells for the five months ended May 31, 1997,
with an ownership of better than 70% average working interest.  The successful
completion of 46 wells continues the company's better than 80% success rate.
Of the 46 wells completed, 20 wells were located in the Permian Basin Region,
eight wells were in the Gulf Coast/East Texas Region, and 18 wells were in the
Rocky Mountain Region.  In addition, the company was in the process of
drilling or completing 21 wells at May 31, 1997.

    Highly Prolific Cotton Valley Reef Drilling Commenced
    The company also reported that it is participating with a 26% working
interest in an exploratory well in the highly prolific Cotton Valley Reef
Trend in the Bear Grass Field, Freestone County, Texas.  The well is scheduled
for a total depth of 14,500 feet to test the Cotton Valley Reef Formation.
Costilla said it anticipates that it will take approximately 105 days to reach
the total depth.

    Sale of High Operating Cost Properties
    Costilla said it completed the sale of various high operating cost wells
resulting in a reduction of lease operating expense per barrel of oil
equivalent (BOE) for the entire company of an estimated $0.25 per BOE.  The
properties sold were producing approximately 600 BOE per day.  The strategy of
replacing older, lower margin production with new well production will
continue to drive lease operating expense per BOE to the company's lower
targeted levels.

    Share Buy Back Initiated
    The company also noted that through the first half of June it had
purchased 78,000 shares of common stock pursuant to its previously announced
stock repurchase program that authorized the purchase of up to 500,000 shares
of stock.

    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.  These factors are discussed
in more detail in the Company's prospectus for its initial public offering of
common stock.
    Costilla Energy Inc. is an independent energy company engaged in the
exploration, acquisition and development of oil and gas properties with
operations primarily in the Permian Basin area of Texas and New Mexico, the
Gulf Coast, and the Rocky Mountain regions.  The Company and its predecessor
have been in business since 1988.

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