AMENDMENT NO. 3 TO ACQUISITION AGREEMENT

EXHIBIT 10.4

AMENDMENT NO. 3 TO ACQUISITION AGREEMENT

THIS AMENDMENT NO. 3 TO ACQUISITION AGREEMENT (this “Amendment”) is entered into as of this 26th day of July, 2011, by and among Mattersight Corporation (f/k/a eLoyalty Corporation), a Delaware corporation (“Seller”), TeleTech Holdings, Inc., a Delaware corporation (“Parent”), and eLoyalty, LLC (f/k/a Magellan Acquisition Sub, LLC), a Colorado limited liability company and a wholly-owned subsidiary of Parent (“Buyer” and, together with Seller and Parent, the “Parties”).

W I T N E S S E T H:

WHEREAS, pursuant to that certain Acquisition Agreement, dated as of March 17, 2011, as amended by that certain Amendment No. 1 thereto, dated as of May 27, 2011, and that certain Amendment No. 2 thereto, dated as of June 20, 2011 (as may be further amended, modified or supplemented from time to time in accordance with the terms thereof, the “Agreement”), by and among the Parties, Buyer agreed to purchase substantially all of the assets of Seller used in or related to the ICS Business;

WHEREAS, the Parties desire to amend the Agreement on the terms and conditions set forth in this Amendment; and

WHEREAS, unless otherwise defined herein, each capitalized term used herein shall have the meaning assigned thereto in the Agreement.

NOW, THEREFORE, in consideration of the foregoing and the respective covenants and agreements set forth herein, and intending to be legally bound hereby, subject to the conditions and other terms herein set forth, the Parties hereby agree as follows:

1. Amendment. The Agreement is hereby amended as follows:

(a) The first sentence of Section 2.7(a) of the Agreement is hereby amended by deleting the words “sixty (60)” and replacing such words with “seventy-five (75)”.

(b) The first sentence of Section 2.7(b) of the Agreement is hereby amended by deleting the words “twenty (20)” and replacing such words with “thirty (30)”.

(c) The second sentence of Section 2.7(b) of the Agreement is hereby amended by deleting the words “twenty (20)” and replacing such words with “thirty (30)”.

2. No Implied Amendments. Except as specifically amended by this Amendment, the Agreement shall remain in full force and effect in accordance with its terms and is hereby ratified and confirmed. All references to “the date hereof” in the Agreement shall continue to refer to the date of the Agreement before any amendment, consent or waiver.

3. Effectiveness of Amendment. This Amendment shall be deemed to be a modification to the Agreement in accordance with Section 10.14 of the Agreement.

4. Benefit of the Amendment. This Amendment shall be binding upon and inure to the benefit of the Parties and their respective successors and permitted assigns.

5. Headings. The headings used in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment.

6. Governing Law. This Amendment shall be governed by, and construed in accordance with, the law of the State of Delaware applicable to contracts to be carried out wholly within such State.

7. Counterparts. This Amendment may be executed simultaneously in multiple counterparts, and in separate counterparts, each of which shall be deemed an original, but all of which taken together shall constitute one and the same instrument.

8. References to Agreement. On and after the date hereof, each reference in the Agreement to “this Agreement,” “hereunder,” “hereof” or words of like import referring to the Agreement shall mean the Agreement as amended by this Amendment.

[signature pages follow]

2

IN WITNESS WHEREOF, the Parties have caused this Amendment No. 3 to Acquisition Agreement to be executed as of the date first above written.

[Signature Page to Amendment No. 3 to Acquisition Agreement]