Exhibit 99.1

Constellation Energy Partners Accelerates

Debt Reduction and Extends Credit Facility

HOUSTON—(BUSINESS WIRE)—June 3, 2011—Constellation Energy Partners LLC (NYSE Arca: CEP) today announced that, in conjunction with extending the maturity date of its reserve-based credit facility by one year, the company has reduced debt by $42 million to $115.5 million outstanding. The cash used to reduce debt was raised by resetting the fixed price on certain hedges related to the company’s 2012 through 2014 natural gas production to $5.75 per MMBtu.

The company also today reaffirmed its 2011 forecast, including guidance on plans to reduce debt $25 million to $30 million this year, which is in addition to the debt reduction announced today.

“We’ve accelerated debt reduction by restructuring our hedges in a way that does not negatively affect our net asset value or impact our strategic focus, operational plans, or capital program for the future,” said Stephen R. Brunner, President and Chief Executive Officer of Constellation Energy Partners. “We’ve now reduced debt by more than $100 million since first announcing plans for debt reduction in 2009. With the additional debt reduction planned for the remainder of this year, we now expect to be below $100 million in debt outstanding by year-end. Our lower level of debt, coupled with our continued operational successes, improving natural gas prices, and a focus on exploiting the oil potential in our asset base, puts us in a position to consider a wider range of opportunities to increase unitholder value.”

Liquidity Update

The company also announced that its lenders have completed their semi-annual review of the borrowing base under its reserve-based credit facility. Pursuant to that review, which takes into account the lower fixed prices stemming from the hedge restructuring, the borrowing base has been set by the lenders at $140.0 million.

Hedge Positions

The hedge restructuring relates to the company’s NYMEX fixed-for-floating price swaps for natural gas production for the period January 2012 through December 2014. There were no changes to any of the company’s other hedges. After resetting the fixed price on NYMEX hedges in place for the period 2012 through 2014, the company maintains the following NYMEX hedges on its 2012 through 2014 natural gas production:

Additional information about the company’s credit facility and hedge program can be found in the company’s filings with the Securities and Exchange Commission and on the company’s Web site (http://www.constellationenergypartners.com).

About the Company

Constellation Energy Partners LLC is a limited liability company focused on the acquisition, development and production of oil and natural gas properties, as well as related midstream assets.

Forward-Looking Statements

We make statements in this news release that are considered forward-looking statements within the meaning of the Securities Act of 1933, as amended, and the Securities Exchange Act of 1934, as amended. These forward-looking statements are largely based on our expectations, which reflect estimates and assumptions made by our management. These estimates and assumptions reflect our best judgment based on currently known market conditions and other factors. Although we believe such estimates and assumptions to be reasonable, they are inherently uncertain and involve a number of risks and uncertainties that are beyond our control. In addition, management’s assumptions about future events may prove to be inaccurate. Management cautions all readers that the forward-looking statements contained in this news release are not guarantees of future performance, and we cannot assure you that such statements will be realized or the forward-looking events and circumstances will occur. Actual results may differ materially from those anticipated or implied in the forward-looking statements due to factors listed in the “Risk Factors” section in our SEC filings and elsewhere in those filings. All forward-looking statements speak only as of the date of this news release. We do not intend to publicly update or revise any forward-looking statements as a result of new information, future events or otherwise. These cautionary statements qualify all forward-looking statements attributable to us or persons acting on our behalf.