<PAGE>

                                                                     Exhibit 4.3

              AGREEMENT OF RESIGNATION, APPOINTMENT AND ACCEPTANCE

      This Agreement of Resignation, Appointment and Acceptance is made by and
among that issuer or other person who is identified in Exhibit A attached hereto
(the "Exhibit") as the "Issuer (the "Issuer"), The Bank of New York, a banking
corporation with trust powers duly organized and existing under the laws of the
State of New York and having its principal corporate trust office at 101 Barclay
Street, New York, NY 10286 (the "Bank") and The Bank of New York Trust Company,
N.A. ("BNYTC"), a national banking association duly organized and existing under
the laws of the United States and having its principal office in Los Angeles,
California.

                                    RECITALS:

      WHEREAS, the Issuer and the Bank entered into one or more trust
indentures, paying agency agreements, registrar agreements, or other relevant
agreements as such are more particularly described in the Exhibit under the
section entitled "Agreements" (individually and collectively referred to herein
as the "Agreements") under which the Bank was appointed in the capacity or
capacities identified in the Exhibit (individually and collectively the
"Capacities");

      WHEREAS, BNYTC has requested that it be appointed by the Issuer as the
successor to the Bank in its Capacities under the Agreements; and

      WHEREAS, BNYTC is willing to accept such appointment as the successor to
the Bank in its Capacities under the Agreements.

      NOW, THEREFORE, the Issuer, the Bank and BNYTC, for an in consideration of
the premises and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, hereby consent and agree as
follows:

                                    ARTICLE I

                                    THE BANK

      SECTION 1.01. The Bank hereby resigns from its Capacities under the
Agreements.

      SECTION 1.02. The Bank hereby assigns, transfers, delivers and confirms to
BNYTC all right, title and interest of the Bank in its Capacity(s) relating to
the Agreements.

                                   ARTICLE II

                                   THE ISSUER

      SECTION 2.01. The Issuer hereby accepts the resignation of the Bank from
its Capacities under the Agreements.

      SECTION 2.02. All conditions relating to the appointment of BNYTC as the
successor to the Bank in its Capacities under the Agreements have been met by
the Issuer, and the Issuer hereby appoints BNYTC to its Capacities under the
Agreements with like effect as if originally named to such Capacities under the
Agreements.

<PAGE>

                                   ARTICLE III

                                      BNYTC

      SECTION 3.01. BNYTC hereby represents and warrants to the Bank and to the
Issuer that BNYTC is not disqualified to act in the Capacities under the
Agreements.

      SECTION 3.02. BNYTC hereby accepts its appointment to the Capacities under
the Agreements and accepts and assumes the rights, powers, duties and
obligations of the Bank under the Agreements, upon the terms and conditions set
forth therein, with like effect as if originally named to such Capacities under
the Agreements.

                                   ARTICLE IV

                                  MISCELLANEOUS

      SECTION 4.01. This Agreement and the resignation, appointment and
acceptance effected hereby shall be effective as of 12:01 A.M. local Los Angeles
time on the Effective Date set forth in the Exhibit.

      SECTION 4.02. This Agreement shall be governed by and construed in
accordance with the laws of the State of Georgia.

      SECTION 4.03. This Agreement may be executed in any number of counterparts
each of which shall be an original, but such counterparts shall together
constitute but one and the same instrument.

      SECTION 4.04. The persons signing this Agreement on behalf of the Issuer,
BNYTC and the Bank are duly authorized to execute it on behalf of the each
party, and each party warrants that it is authorized to execute this Agreement
and to perform its duties hereunder.

      SECTION 4.05. The Issuer represents that it is the type of entity as
identified in the Exhibit and has been duly organized and is validly existing
under the laws of the jurisdiction and with the principal office as identified
in the Exhibit.

                                      -2-
<PAGE>

      IN WITNESS WHEREOF, the parties hereto have caused this Agreement of
Resignation, Appointment and Acceptance to be duly executed and acknowledged all
as of the day and year first above written.

                                       COX COMMUNICATIONS, INC.

                                       By:   /s/ Susan W. Coker
                                             ----------------------------------
                                       Name: Susan W. Coker
                                       Title Vice President and Treasurer

                                       THE BANK OF NEW YORK

                                       By:    /s/ Lee Ann Willis
                                              ---------------------------------
                                       Name:  Lee Ann Willis
                                       Title: Agent

                                       THE BANK OF NEW YORK TRUST COMPANY, N.A.

                                       By:    /s/ Karen Z. Kelly
                                              ---------------------------------
                                       Name:  Karen Z. Kelly
                                       Title: Vice President

                                      -3-
<PAGE>

                                    EXHIBIT A

Issuer: Cox Communications, Inc.

Effective Date: April 27, 2005

Agreement(s): Indenture dated as of June 27, 1995 and Supplemental Indentures

Cox Communications, Inc.   6.875% Notes Due June 15, 2005
Cox Communications, Inc.   7.625% Debentures Due June 15, 2025
Cox Communications, Inc.   7.75% Notes Due August 15, 2006
Cox Communications, Inc.   3.875% Notes Due October 1, 2008
Cox Communications, Inc.   6.4% Notes Due August 1, 2008
Cox Communications, Inc.   7.875% Notes Due August 15, 2009
Cox Communications, Inc.   7.75% Notes Due November 1, 2010
Cox Communications, Inc.   6.75% Notes Due March 15, 2011
Cox Communications, Inc.   4.625% Notes Due June 1, 2013
Cox Communications, Inc.   5.5% Notes Due October 1, 2015
Cox Communications, Inc.   7.25% Debentures Due November 15, 2015
Cox Communications, Inc.   Exchangeable Sub Discount Debs Due 2020
Cox Communications, Inc.   6.8% Debentures Due August 1, 2028
Cox Communications, Inc.   Medium Term Note Series A-6.85% Due January 15, 2018
Cox Communications, Inc.   Medium Term Notes Series A-6.95% Due January 15, 2028
Cox Communications, Inc.   Medium Term Notes Series A-7.19% Due August 9, 2006
Cox Communications, Inc.   Medium Term Notes Series A-7.03% Due November 6, 2006
Cox Communications, Inc.
Cox Comm. Inc.
  (Times Mirror Company)   7.125% Notes Due March 1, 2013
Cox Comm. Inc.
  (Times Mirror Company)   7.375% Debentures Due July 1, 2023
Cox Communications, Inc.   7.125% Notes Due October 1, 2012
Cox Communications, Inc.   4.625% Notes Due January 15, 2010
Cox Communications, Inc.   5.450% Notes Due December 15, 2014
Cox Communications, Inc.   Floating Rate Notes Due 2007

                                       A-1