2012 AMENDMENT TO THE ENSCO INTERNATIONAL INCORPORATED 1998 INCENTIVE PLAN (As Amended on August 23, 2011, and As Assumed by Ensco plc as ofDecember 23, 2009)

Exhibit 10.2

2012 AMENDMENT TO THE

ENSCO INTERNATIONAL INCORPORATED

1998 INCENTIVE PLAN

(As Amended on August 23, 2011, 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 1998 Incentive Plan, effective May 12, 1998 (which, as previously amended from time to time is referred to herein as the “Plan”);

WHEREAS, the Plan was 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 Amendment to the Plan by unanimous written consent on May 8, 2012; and

WHEREAS, the Company now desires to adopt this 2012 Amendment to the Plan in order to (i) delete the definitions of “ADR” and “ADS” in Section 2 of the Plan, and (ii) amend the definition of “Share” in Section 2 of the Plan;

NOW, THEREFORE, in consideration of the premises and covenants herein contained, the Company hereby adopts the following 2012 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 one Class A ordinary share of the Company, nominal value US$0.10 per Share. All references to in the Plan to shares of common stock, stock, shares of Ensco Delaware, American depositary shares, and/or ADSs shall be read and considered to be references to Class A ordinary shares of the Company 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 Class A ordinary shares of the Company, unless the context otherwise requires, and all provisions of the Plan shall be consistently interpreted and applied.

[signatures on next page]

IN WITNESS WHEREOF, the Company has caused this 2012 Amendment to the ENSCO International Incorporated 1998 Incentive Plan to be signed on its behalf by and a its duly authorized officer, effective as first above written.