Exhibit 99.1

For further information
Contact John S. Weatherly, CFO 1-800-451-1294


FOR IMMEDIATE RELEASE
_____________________

Callon Petroleum Company Announces Stock Buyback Program

Natchez, MS (September 2, 1998) - Callon Petroleum Company (NYSE: CPE/CPE.PrA)
announced today that its Board of Directors has authorized the repurchase of
up to $10 million in common stock.  The purchases may be made on the open
market or in privately negotiated transactions, depending upon market
conditions and other factors.  Callon has approximately 8,039,000 shares
outstanding.  Repurchased shares will be held in the company's treasury and
used for general corporate purposes.

The company's ability to purchase common stock currently is limited by covenants
in its 10.125% Senior Subordinated Notes.  The amount the company may repurchase
under these covenants will increase or decrease in the future based upon, 
among other things, earnings and losses sustained by the company.

Fred L. Callon, president and CEO, explains the decision was made "because 
we believe the stock is undervalued.  This gives us an opportunity to buy at a
significant discount when you consider both our net asset value and book value 
per share are substantially above the current market value.  This stock
repurchase program is just another example of our confidence in the planned
growth of the company."

Callon Petroleum Company has been engaged in the exploration, development, 
acquisition and operation of oil and gas properties in the Gulf Coast region 
since 1950.

This news release contains forward-looking statements within the meaning of 
Section 27A of the Securities Act of 1933 and Section 21E of the Securities 
Exchange Act of 1934, including statements regarding the company's intent to
repurchase its common stock and the amount of such repurchases.  The company
can give no assurances that the assumptions upon which such forward-looking
statements are based will prove to have been correct.  Important factors that
could cause actual results to differ materially from the company's expectations
("Cautionary Statements") include the volatility of oil and gas prices and
markets, risks inherent in exploring for, developing and producing oil and
gas and the effect of governmental, environmental and other regulations.
These factors are further described in Callon's filings with the Securities
and Exchange Commission, including its Annual Reports on Form 10-K.