Exhibit 32.1

Certification Pursuant to Section 1350 of Chapter 63

of Title 18 of the United States Code

I, LeRoy T. Carlson, Jr., the chief executive officer of Telephone and Data Systems, Inc., certify that (i) the annual report on Form 10-K/A for the year ended December 31, 2004 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-K/A fairly presents, in all material respects, the financial condition and results of operations of Telephone and Data Systems, Inc.

/s/ LEROY T. CARLSON, JR.

LEROY T. CARLSON, JR.

April 26, 2006

A signed original of this written statement required by Section 906 of the Sarbanes-Oxley Act of 2002 has been provided to Telephone and Data Systems, Inc. and will be retained by Telephone and Data Systems, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.