Exhibit 10.57

J U N E A U E X P L O R A T I O N L . P .

John W. Burke
Vice President-Land                            e-mail:
jburke@juneauexploration.com
June 8, 2012

Contango Operators, Inc.
3700 Buffalo Speedway, Suite 960
Houston, TX 77098

Attention: Mr. Sergio Castro

Re:    Jim Hogg County Exploration Agreement

Dear Mr. Castro,

Juneau Exploration L.P. (JEX) has provided to Contango Operators, Inc. (COI) a
copy of a letter agreement dated May 11, 2012 between JEX and a third party
(Letter Agreement) outlining the general terms and provisions of an exploration
program involving horizontal exploration of the Upper and Lower Queen City
Horizons and the Yegua Horizon within the Area of Mutual Interest described on
Exhibit “A” attached thereto.

COI by its execution herein below, hereby agrees to enter into this agreement
with JEX to assume all of the benefits as well as all of the risks, expenses and
liabilities of JEX in the above described Letter Agreement.

As consideration, COI hereby agrees JEX shall be entitled to receive a 10%
carried working interest through the tanks, proportionately reduced to COI’s
working interest, on all of the promoted wells provided for in the Letter
Agreement after COI has received payout of their original investment costs on a
well by well basis. On the unpromoted wells provided for in the Letter
Agreement, COI hereby agrees JEX shall receive a 10% carried working interest
through the tanks, proportionately reduced to COI’s working interest.

As an example, on promoted wells, COI shall pay 90% of the costs to earn 50%
working interest in the wells. COI’s working interest in the unpromoted wells
shall be 50% working interest. JEX’s 10% carry through the tanks shall be 10% of
COI’s 50% or a 5% working interest. JEX shall be entitled to receive its 5%
working interest after the payout described above on the promoted wells and
shall receive its 5% working interest on the unpromoted wells effective with the
first production after the costs of drilling, fracing, completing and the
installation of the flowlines, tank batteries and all costs to commence first
production have been expended by COI.

Additionally COI agrees certain employees of JEX shall be entitled to retain an
overriding royalty interest of 2.5%, on the leases assigned or owned by COI,
proportionately reduced to COI’s working interest.

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JEX and COI agree to enter into further contracts and documents, as necessary,
in the event more agreements are entered into between JEX and the third party to
further define the terms and provisions of the Letter Agreement.

Please indicate your agreement to the above terms and conditions by executing
below.

Sincerely,

/s/ JOHN W. BURKE
John W. Burke
Vice President-Land

ACCEPTED AND AGREED
 
this 11th day of June, 2012.

CONTANGO OPERATORS, INC.

By: /s/ SERGIO CASTRO
Sergio Castro    
Vice President

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