Exhibit 10.1

Eagle Rock Energy G&P, LLC

A subsidiary of Eagle Rock Energy Partners, L.P.

May 21, 2015

Mr. Joseph A. Mills

Dear Joe:

This agreement is entered into by and between you and Eagle Rock Energy G&P, LLC (“G&P”) and sets forth certain amendments to the Confidentiality and Noncompete Agreement entered into between you and G&P dated as of August 3, 2012 (the “Confidentiality and Noncompete Agreement”).

This agreement, and the amendments set forth herein, shall be effective upon the closing (the “Closing”) of that certain contemplated Agreement and Plan of Merger (the “Merger Agreement”) by and among Vanguard Natural Resources, LLC, a Delaware limited liability company (“Parent”), Talon Merger Sub, LLC, a Delaware limited liability company and wholly owned indirect subsidiary of Parent, Eagle Rock Energy Partners, L.P., a Delaware limited partnership, and Eagle Rock GP, L.P., a Delaware limited partnership.  For the avoidance of doubt, if the Closing does not occur, this letter agreement will be of no force or effect.

By signing below, you and G&P acknowledge and agree that, effective as of the Closing, the Confidentiality and Non-Competition Agreement is hereby amended in the following manner:

1.                                      The term “Company,” as used in the Confidentiality and Noncompete Agreement is amended so that it means: “the Partnership, G&P, GP and its and their direct and indirect subsidiaries as exist as of May 21, 2015.”

2.                                      Section 4(f) of the Confidentiality and Noncompete Agreement is amended in order to delete the parenthetical “(or person who within the preceding 90 days was an employee)” so that, as amended, Section 4(f) of the Confidentiality and Noncompete Agreement reads, in its entirety:

“(f)                       Employee will not, during the eighteen month period following the Termination Date, solicit, entice, persuade or induce, directly or indirectly, any employee of the Company or any other person who is under contract with or rendering services to the Company, to (i) terminate his or her employment by, or contractual relationship with, the Company, (ii) refrain from extending or renewing the same (upon the same or new terms), (iii) refrain from rendering services to or for the Company, (iv) become

employed by or enter into contractual relations with any Persons other than the Company, or (v) enter into a relationship with a competitor of the Company.”

By signing below, you and G&P acknowledge and agree that the Confidentiality and Noncompete Agreement, as now exists and as may be amended by this agreement, remains in full force and effect and is enforceable in all respects.