THIRD AMENDMENT TO THE ENSCO INTERNATIONAL INCORPORATED 2005 LONG-TERM INCENTIVE PLAN (As Revised and Restated onDecember 22, 2009 and As Assumed by Ensco plc as of December 23, 2009)

Exhibit 10.1

THIRD AMENDMENT

TO THE

ENSCO INTERNATIONAL INCORPORATED

2005 LONG-TERM INCENTIVE PLAN

(As Revised and Restated on December 22, 2009 and

As Assumed by Ensco plc as of December 23, 2009)

THIS AMENDMENT is effective the 14^th of May 2012, by Ensco plc, having its principal office in London, England (hereinafter referred to as the “Company”).

WITNESSETH:

WHEREAS, ENSCO International Incorporated adopted the ENSCO International Incorporated 2005 Long-Term Incentive Plan (the “Plan”) effective January 1, 2005;

WHEREAS, the Plan was revised and restated on December 22, 2009, and was subsequently assumed by the Company effective as of December 23, 2009;

WHEREAS, the Board of Directors of the Company (the “Board”) has authorized and approved this Third Amendment to the Plan by unanimous written consent on May 8, 2012; and

WHEREAS, the Company now desires to adopt this Third Amendment to the revised and restated Plan for the purpose of (i) deleting the definitions of “ADR” and “ADS” in Section 2 of the Plan, (ii) amending the definition of “Share” in Section 2 of the Plan, and (iii) amending Section 5(a) of the Plan to remove references to shares held in reserve by a subsidiary of the Company;

NOW, THEREFORE, in consideration of the premises and covenants herein contained, the Company hereby adopts the following Third Amendment to the Plan:

1. Section 2 of the Plan is hereby amended by deleting the definitions of “ADR” and “ADS.”

2. The definition of “Share” in Section 2 of the Plan is hereby amended in its entirety to read as follows:

“Share” shall mean a Class A ordinary share of the Company, nominal value US$0.10 per Share. All references in the Plan to ADSs shall be read and considered to be references to Shares, unless the context otherwise requires, and all references (specific or otherwise) to “stockholders of the Company” shall be read and considered to be references to holders of Shares, unless the context otherwise requires, and all provisions of the Plan shall be consistently interpreted and applied.

3. Section 5(a) of the Plan is hereby amended to read as follows:

(a) Basic Limitation. Shares offered or subject to Awards granted under this Plan, or issued in settlement of Performance Unit Awards granted under this Plan, may be authorized but unissued Shares or Shares that have been acquired by the trustees of any employee benefit trust established in connection with this Plan. Subject to adjustment pursuant to Section 10, the aggregate number of Shares that are available for issuance under this Plan shall not exceed ten million (10,000,000) Shares (the “Plan Maximum”). Effective November 4, 2008, as approved by a vote at the 2009 annual meeting of the ENSCO International Incorporated stockholders (the “2009 Annual Meeting”) of the owners of at least a majority of the shares of common stock of ENSCO International Incorporated, present in person or by

proxy and entitled to vote at the 2009 Annual Meeting, (i) Restricted Share Awards, all of which can be issued as Performance Awards, and Performance Unit Awards on no more than six million (6,000,000) Shares, and (ii) Options on no more than the number of Shares equal to the difference between the Plan Maximum and the actual aggregate number of Shares issued as Restricted Share Awards and in settlement of Performance Unit Awards and, in each case, subject to adjustment pursuant to Section 10 of this Plan, may be issued under this Plan. The Committee shall not issue more Shares than are available for issuance under this Plan. The number of Shares that are subject to unexercised Options at any time under this Plan shall not exceed the number of Shares that remain available for issuance under this Plan. The Company, during the term of this Plan, shall at all times reserve and keep available sufficient Shares to satisfy the requirements of this Plan. Shares shall be deemed to have been issued under this Plan only to the extent actually issued and delivered pursuant to an Award; provided, however, in no event shall any Shares that have been subject to Options or Restricted Share Awards be returned to the number of Shares available under this Plan Maximum for distribution in connection with the same type of future Awards by reason of such Shares (i) being withheld, if permitted under Section 3(b)(xii) and Section 6(f)(ii), from the total number of Shares to be issued upon the exercise of Options as payment of the Exercise Price of such Options, or (ii) being withheld, if permitted under Section 3(b)(xiii) and Section 9(b), from the total number of Shares to be issued upon the exercise of Options, the vesting or settlement of any Restricted Share Awards or the settlement of any Performance Unit Awards to meet the withholding obligations related to such exercises, vesting and settlement. Nothing in this Section 5(a) shall impair the right of the Company to reduce the number of outstanding Shares pursuant to repurchases, redemptions, or otherwise; provided, however, that no reduction in the number of outstanding Shares shall (i) impair the validity of any outstanding Award, whether or not that Award is fully vested, exercisable, or earned and payable or (ii) impair the status of any Shares previously issued pursuant to an Award as duly authorized, validly issued, fully paid, and nonassessable. The Shares to be delivered under this Plan shall be made available from (a) authorized but unissued Shares, or (b) Shares forfeited under this Plan that are held in an employee benefit trust, in each situation as the Committee may determine from time to time in its sole discretion.

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IN WITNESS WHEREOF, the Company has caused this Third Amendment to the ENSCO International Incorporated 2005 Long-Term Incentive Plan to be signed on its behalf by and a its duly authorized officer, effective as first above written.