Exhibit 99.1

Constellation Energy Partners Reports

First Quarter 2012 Results

HOUSTON—(BUSINESS WIRE)—May 10, 2012—Constellation Energy Partners LLC (NYSE Amex: CEP) today reported first quarter 2012 results.

The company produced 3,226 MMcfe during the first quarter for average daily net production of 35.5 MMcfe for the quarter. Net oil production for the first quarter was 324 barrels per day, or approximately 29.5 thousand barrels in total, which represents an increase of approximately 3% over the prior quarter’s total oil production.

Revenue of $23.8 million for the first quarter 2012 includes revenue from sales of $10.2 million, of which approximately 69% was from natural gas sales and 31% was from oil sales. The balance of the company’s first quarter 2012 revenue came from hedge settlements ($6.1 million), services provided to third parties ($0.9 million), and gains on mark-to-market activities ($6.6 million), which is a non-cash item.

Operating costs, which include lease operating expenses, production taxes and general and administrative expenses, net of certain non-cash items, averaged $3.40 per Mcfe for the first quarter 2012, which is a 3% improvement versus the first quarter of 2011.

Adjusted EBITDA for the first quarter 2012 was $5.9 million. On a GAAP basis, the company recorded net income of $5.9 million for the quarter.

The company completed 17 net wells and recompletions using $2.7 million in cash flow from operations during the first quarter 2012. Drilling activities in 2012 continue to focus on oil potential in the company’s existing asset base as well as capital efficient recompletions. The company finished the first quarter of 2012 with 38 net wells and recompletions in progress.

“We made solid progress on executing this year’s plan to add oil production during the first quarter,” said Stephen R. Brunner, President and Chief Executive Officer of Constellation Energy Partners. “Based on the results of our drilling efforts and our available inventory of oil opportunities, we continue to pursue our capital plan for 2012. We anticipate that this plan will enable us to further diversify our production and revenue mix, thereby increasing the contribution of oil production to our financial results this year.”

Distribution Outlook

The decision to reinstate any future quarterly distributions will consider, among other things, the company’s outstanding borrowings under the reserve-based credit facility and cash reserves that are set by the company’s board of managers for the proper conduct of its business. All distributions are subject to approval by the company’s board of managers.

Financial Outlook for 2012

The company forecasts capital spending of between $15.0 million and $19.0 million in 2012. Of this amount, $15.0 million is maintenance capital.

Net production is forecast to range between 13.3 and 14.1 Bcfe for 2012, with operating costs forecast to range between $42.5 million and $46.0 million for the year.

With additional hedges added in March 2012, the company has hedged approximately 78% of the midpoint of its production forecast, including hedges for the balance of 2012 on 5.0 Bcfe of our Mid-Continent natural gas production at an average price, including basis, of $4.73 per Mcfe, 3.0 Bcfe of our remaining natural gas production at an average price of $5.27 per Mcfe, and 67 MBbl of our oil production at an average price of $103.38 per barrel.

Additional detail on the company’s 2012 forecast can be found in the tables included with the company’s fourth quarter and full year 2011 news release dated Feb. 29, 2012.

- 2 -

Conference Call Information

The company will host a conference call at 8:30 a.m. (CDT) on Thursday, May 10, 2012 to discuss first quarter 2012 results.

To participate in the conference call, analysts, investors, media and the public in the U.S. may dial (800) 857-0653 shortly before 8:30 a.m. (CDT). The international phone number is (773) 799-3268. The conference password is PARTNERS.

A replay will be available beginning approximately one hour after the end of the call by dialing (866) 360-7726 or (203) 369-0178 (international). A live audio webcast of the conference call, presentation slides and the earnings release will be available on Constellation Energy Partners’ Web site (www.constellationenergypartners.com) under the Investor Relations page. The call will also be recorded and archived on the site.

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.

SEC Filings

The company intends to file its first quarter 2012 Form 10-Q on or about May 10, 2012.

Non-GAAP Measures

We present Adjusted EBITDA in addition to our reported net income (loss) in accordance with GAAP. Adjusted EBITDA is a non-GAAP financial measure that is defined as net income (loss) adjusted by interest (income) expense, net; depreciation, depletion and amortization; write-off of deferred financing fees; asset impairments; accretion expense; (gain) loss on sale of assets; exploration costs; (gain) loss from equity investment; unit-based compensation programs; (gain) loss from mark-to-market activities; and unrealized (gain) loss on derivatives/hedge ineffectiveness.

Adjusted EBITDA is used as a quantitative standard by our management and by external users of our financial statements such as investors, research analysts and others to assess the financial performance of our assets without regard to financing methods, capital structure or historical cost basis; the ability of our assets to generate cash sufficient to pay interest costs and support our indebtedness; and our operating performance and return on capital as compared to those of other companies in our industry, without regard to financing or capital structure.

- 3 -

Adjusted EBITDA is not intended to represent cash flows for the period, nor is it presented as a substitute for net income, operating income, cash flows from operating activities or any other measure of financial performance or liquidity presented in accordance with GAAP.

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.

- 4 -

Constellation Energy Partners LLC

Operating Statistics

- 5 -

Constellation Energy Partners LLC

Condensed Consolidated Statements of Operations

- 6 -

Constellation Energy Partners LLC

Condensed Consolidated Balance Sheets

- 7 -

Constellation Energy Partners LLC

Reconciliation of Net Income (Loss) to Adjusted EBITDA

We define Adjusted EBITDA as net income (loss) plus:

- 8 -