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                                                                     EXHIBIT 3.4


                            CERTIFICATE OF AMENDMENT
                                       OF
                          CERTIFICATE OF INCORPORATION
                                       OF
                            COX COMMUNICATIONS, INC.


COX COMMUNICATIONS, INC., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware (the
"Corporation"),

DOES HEREBY CERTIFY:

FIRST: That, the Board of Directors of COX COMMUNICATIONS, INC. pursuant to
Sections 141 and 242 of the General Corporation Law, duly adopted resolutions
setting forth a proposed amendment to the Certificate of Incorporation of said
Corporation, declaring said amendment to be advisable and submitting the
proposed amendment to the stockholders of the Corporation for consideration
thereof. The stockholders of the Corporation duly approved, pursuant to said
Section 242, said proposed amendment at the annual meeting of the stockholders
on May 16, 2000. The resolutions setting forth the amendment to the Certificate
of Incorporation are as follows:

         RESOLVED, that, subject to stockholder approval, the Certificate of
Incorporation of the Corporation be amended by filing the Certificate of
Amendment such that subsection A of Article V thereof shall be restated in its
entirety to read as follows: "A. Authorized Shares. The total number of shares
of all classes of capital stock that the Corporation shall have authority to
issue is seven hundred forty-three million (743,000,000) shares of which (i)
seven hundred thirty-three million (733,000,000) shares of a par value of $1.00
per share shall be Common Stock (the "Common Stock"), and (ii) ten million
(10,000,000) shares of a par value of $1.00 per share shall be Preferred Stock
(the "Preferred Stock"). The Common Stock shall be divided into classes as
follows: six hundred seventy-one million (671,000,000) shares of Class A Common
Stock ("Class A Stock") and sixty-two million (62,000,000) shares of Class C
Common Stock ("Class C Stock").";

         FURTHER RESOLVED, that the proper officers of the Corporation be, and
they each (acting alone) hereby are, authorized to file the Certificate of
Amendment with the Secretary of State of the State of Delaware promptly after
the requisite stockholder approval has been obtained; and

         FURTHER RESOLVED, that the foregoing amendments to the Certificate of
Incorporation of the Corporation, subject to approval by the stockholders of the
Corporation, shall be effective upon the filing of a Certificate of Amendment to
the Certificate of Incorporation of the Corporation setting forth the foregoing
amendments with the Secretary of State of the State of Delaware.

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SECOND: That said amendment was approved by the requisite vote of the
stockholders of the Corporation at the annual meeting of stockholders of the
Corporation.

THIRD:  That said amendment was duly adopted in accordance with the provisions
of Section 242 of the General Corporation Law of the State of Delaware.

FOURTH:  That the capital of said Corporation shall not be reduced under or by
reason of said amendments.



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         IN WITNESS WHEREOF, said COX COMMUNICATIONS, INC. has caused this
certificate to be signed by James O. Robbins, its President and Chief Executive
Officer, and Andrew A. Merdek, its Secretary, this 16th day of May, 2000.



                                                By:/s/ James O. Robbins
                                                   -----------------------------
                                                   James O. Robbins
                                                   President and Chief
                                                   Executive Officer




ATTEST: /s/ Andrew A. Merdek
       ---------------------------
       Andrew A. Merdek
       Secretary