Exhibit 10.1

THIRD AMENDMENT TO RESTRUCTURING SUPPORT AGREEMENT

This THIRD AMENDMENT (this “Third Amendment”) to the Restructuring Support
Agreement, dated as of October 20, 2016, by and among (i) the Stone Parties (as
defined therein) and (ii) the Consenting Noteholders (as defined therein), as
amended by that certain First Amendment to the Restructuring Support Agreement,
dated as of November 4, 2016 (the “First Amendment”) and that certain Second
Amendment to the Restructuring Support Agreement, dated as of November 9, 2016
(the “Second Amendment”) (together with the schedules, annexes and exhibits
(including the term sheet) attached thereto, as amended by the First Amendment
and further amended by the Second Amendment, the “Restructuring Support
Agreement”), is being entered into as of November 15, 2016, by and among (i) the
Stone Parties and (ii) the undersigned Consenting Noteholders. This Third
Amendment collectively refers to the Stone Parties and the Consenting
Noteholders as the “Parties” and each individually as a “Party.” Capitalized
terms used but not defined herein shall have the meanings ascribed to them in
the Restructuring Support Agreement.

WHEREAS, the Parties desire to further amend the terms of the Restructuring
Support Agreement to (i) add a termination right, for the benefit of the
Consenting Noteholders, with respect to additions, deletions and modifications
to the Specified Employee Plans and the Indemnification Provisions; and
(ii) further extend the deadline for commencement of the solicitation in respect
of the Plan as set forth on Schedule 1 from November 15, 2016, to November 17,
2016 (collectively, the “Proposed Amendment”);

WHEREAS, pursuant to Section 28 of the Restructuring Support Agreement, the
Proposed Amendment requires the prior written consent of the Stone Parties and
the Required Consenting Noteholders; and

WHEREAS, the undersigned Consenting Noteholders, taken as a whole, satisfy the
definition of Required Consenting Noteholders as it applies to the Proposed
Amendment.

NOW, THEREFORE, in consideration of the promises, mutual covenants, and
agreements set forth herein, and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, each of the Parties,
intending to be legally bound, hereby agrees as follows:

 

  1. Amendment to Section 8. Section 8 of the Restructuring Support Agreement
be, and it hereby is, amended as follows:

 

  a. subsections (n) and (o) be, and each of them hereby is, amended such that
(i) the word “or” at the end of subsection (n) is deleted, and (ii) the final
period at the end of subsection (o) be replaced with a semi-colon followed by
the word “or”; and

 

  b. a newly created subsection (p) be, and it hereby is, added to Section 8 of
the Restructuring Support Agreement, which shall read as follows:

“if (i) the additions, deletions and modifications to the Specified Employee
Plans are not acceptable to the Required Consenting Noteholders in their sole
discretion, and (ii) the additions, deletions and modifications to the

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Indemnification Provisions for the purpose of making such Indemnification
Provisions consistent with current market practice are not reasonably
satisfactory to the Required Consenting Noteholders.”

 

  2. Amendment to Schedule 1. The first paragraph (paragraph (a)) of Schedule 1
of the Restructuring Support Agreement be, and it hereby is, amended and
restated in its entirety to read:

“the Stone Parties shall commence the solicitation in respect of the Plan, no
later than November 17, 2016;”

 

  3. Miscellaneous.

 

  a. Sections 15 (Fees and Expenses), 16 (Consents and Acknowledgments), 18
(Survival of Agreement), 19 (Settlement), 20 (Relationship Among Parties), 21
(Specific Performance), 22 (Governing Law and Consent to Jurisdiction and
Venue), 23 (WAIVER OF RIGHT TO TRIAL BY JURY), 24 (Successors and Assigns), 25
(No Third-Party Beneficiaries), 26 (Notices), 28 (Amendments), 29 (Reservation
of Rights), 30 (Counterparts), 31 (Public Disclosure), 32 (Creditors’
Committee), 33 (Severability), 35 (Time Periods), 36 (Headings), 37
(Interpretation) and 38 (Remedies Cumulative; No Waiver) be, and each of them
hereby is, incorporated by reference, mutatis mutandis, as if such provisions
were set forth fully herein.

 

  b. This Third Amendment, together with the Restructuring Support Agreement, as
amended hereby, constitute the complete and exclusive statement of agreement
among the Stone Parties and the Consenting Noteholders with respect to the
subject matter hereof and thereof, and supersede all prior written and oral
statements by and among the Stone Parties and the Consenting Noteholders or any
of them.

 

  c. Except as specifically amended hereby, the Restructuring Support Agreement
shall remain in full force and effect.

[Signature pages follow]

 

2

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IN WITNESS WHEREOF, the Parties have executed this Amendment as of the date set
forth above.

 

STONE ENERGY CORPORATION, a Delaware corporation By:  

/s/ Kenneth H. Beer

  Kenneth H. Beer, Executive Vice President and Chief Financial Officer

STONE ENERGY OFFSHORE, L.L.C.,

a Delaware limited liability company, by

Stone Energy Corporation, its sole member By:  

/s/ Kenneth H. Beer

  Kenneth H. Beer, Executive Vice President and Chief Financial Officer

STONE ENERGY HOLDING, L.L.C.,

a Delaware limited liability company, by

Stone Energy Corporation, it sole member By:  

/s/ Kenneth H. Beer

  Kenneth H. Beer, Executive Vice President and Chief Financial Officer

[Signature Page to Amendment to Restructuring Support Agreement – Stone Parties]