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                                                                    EXHIBIT 10.2

                             AMENDMENT NUMBER THREE
                                     TO THE
                            COX COMMUNICATIONS, INC.
                            LONG-TERM INCENTIVE PLAN

         Pursuant to the power of Cox Communications, Inc. (the "Company") to
amend the Cox Communications, Inc. Long-Term Incentive Plan (the "Plan"), the
Plan hereby is amended as follows:

                                       1.

         Section 4 of the Plan is amended by deleting the first sentence thereof
in its entirety and by substituting the following therefor:

         "Subject to adjustment as provided in Section 10, the total number of
         Shares reserved and available for Awards under the Plan shall be
         24,000,000."

                                       2.

         The effective date of this Amendment Number Three is the date the
Amendment is adopted by the Compensation Committee of the Board of Directors of
the Company; subject, however, to the approval of the Amendment by the
shareholders of the Company at the annual shareholder meeting of the Company to
be held in the year 2000.<PAGE>   1
                                                                    Exhibit 10.3

                            COX COMMUNICATIONS, INC.
                             ANNUAL INCENTIVE PLAN
                   AMENDED AND RESTATED AS OF JANUARY 1, 2000

         This Cox Communications, Inc. Annual Incentive Plan (the "Plan"),
which shall be effective as of January 1, 1997, is designed to provide
incentive benefits to designated senior management employees of Cox
Communications, Inc. ("Cox"). The Plan amends and restates the Cox Annual
Incentive Plan, as initially in effect as of January 1, 1997.

1.       DEFINITIONS

         For purposes of the Plan, the following terms shall have the meanings
set forth below:

         (a) "Award" means the amount of cash bonus payable under the Plan to a
Participant with respect to a Plan Year.

         (b) "Board" means the Board of Directors of Cox.

         (c) "Committee" means the Compensation Committee of the Board.

         (d) "Earned Target Percentage" means the percentage of the Target
Bonus that is earned and payable to a Participant under the provisions of the
Plan with respect to a Plan Year, which is based on the achievement of one or
more Performance Goals.

         (h) "Participant" means any senior management employee of Cox
designated as a Participant by the Committee.

         (f) "Performance Goals" means one or more objective measurable
performance factors as determined by the Committee each Plan Year based upon
one or more factors, including revenue, revenue generating units, commercial
units, operating cash flow, earnings, economic profit, return on investment,
number of subscribers, customer service, net income, earnings per share and
stock price.

         (i) "Plan" means the Cox Communications, Inc. Annual Incentive Plan,
as amended from time to time.

         (j) "Plan Year" means the calendar year.

         (k) "Target Bonus" means for a Plan Year beginning on or after January
1, 2000, an amount of cash bonus equal to a percent of a Participant's base
compensation for the Plan Year, which percent shall be established by the
Committee.

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2.       ADMINISTRATION

         The Plan shall be administered by the Committee, which shall have the
discretionary authority to interpret the provisions of the Plan, including all
decisions on eligibility to participate, establishment of the Target Bonus,
payment targets and the amount of Awards payable under the Plan. A writing
signed by all members of the Committee shall constitute an act of the Committee
without the necessity of a meeting. The intention of Cox and the Committee is to
administer the Plan in compliance with Section 162(m) of the Internal Revenue
Code (the "Code") so that Awards paid under the Plan will be treated as
performance-based compensation, as that term is defined in Code Section
162(m)(4)(C). If any provision of the Plan does not comply with the requirements
of Section 162(m) of the Code, then such provision shall be construed or deemed
amended to the extent necessary to conform to such requirements. The decisions
of the Committee shall be final and binding on all parties.

3.       ESTABLISHMENT OF EARNED TARGET PERCENTAGE

         With respect to each Plan Year, the Committee will establish a schedule
of Performance Goals, and will establish an objective methodology to derive the
Target Performance Percentage. The objective methodology shall determine the
Earned Target Percentage based directly and exclusively on the level of the
designated Performance Goals achieved for a Plan Year. The designated
Performance Goals and the objective methodology to be used with respect to a
Plan Year shall be established in writing by the Committee within 90 days of the
beginning of the Plan Year.

4.       CALCULATION OF AWARD

         (a) With respect to each Plan Year, the amount of an Award payable to
any Participant will be calculated by multiplying the Participant's Target Bonus
by the Earned Target Percentage for such Plan Year. The maximum amount of an
Award that can be paid under the Plan for any Plan Year shall be $2,000,000.

         (b) If a Participant either terminates employment, including on account
of retirement or disability, or dies during a Plan Year, then the Participant,
or the Participant's beneficiary, shall be entitled to receive a pro rata share
of the Award otherwise payable thereto with respect to the Plan Year. The amount
of the pro rata Award payable under this Paragraph 4(b) shall be determined by
multiplying the Award otherwise payable under the Plan by a fraction, the
numerator of which is the number of days during the Plan Year that the
Participant was employed preceding the date of termination or death and the
denominator of which is 365.

         (c) Notwithstanding any provisions of the Plan to the contrary, the
Committee reserves the right, in its sole discretion, to reduce or eliminate the
amount of an Award otherwise payable to a Participant with respect to a Plan
Year.

5.       DISTRIBUTIONS

         (a) At the sole discretion of the Committee, distribution of each Award
shall be made by Cox either (1) in a lump sum cash payment, (2) in the form of
shares of common stock of Cox, which shares may be subject to certain
restrictions upon issue that impose a risk of forfeiture or (3) some combination
of cash and common stock; provided, that the issuance of shares of common stock
may be made only to the extent permissible under applicable securities laws. In
the event any distribution is made in the form of Cox common stock, the value of
the common stock so issued may not exceed the total amount of the Award to be
made under this Plan, and the value of any fractional shares of common stock
shall be distributed in cash. The Committee, acting in its sole discretion, may
determine the terms and conditions of restrictions, if any, that shall be
applied to the common stock issued hereunder. Any distribution made under this
Plan shall occur within a reasonably practicable period of time after the end of
the Plan Year in which the Participant has earned the Award; provided, that no
Award shall become payable to a Participant with respect to any Plan Year until
the Committee has certified in writing that the terms and conditions underlying
the payment of such Award have been satisfied. If a Participant entitled to the
payment of an Award under the Plan dies prior to the distribution of such Award,
the distribution shall be made to the Participant's beneficiary, as designated
under the Plan, within the same time period in which the Award otherwise would
have been paid to the Participant.

                                      -2-
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         (b) Notwithstanding any provisions of the Plan to the contrary, no
Award shall be payable to a Participant with respect to the Plan Year commencing
on January 1, 2000 unless and until the Plan is approved by the majority vote of
the shareholders of Cox voting with respect to the approval of the Plan in
accordance with applicable Federal securities laws. The Committee reserves the
right to precondition the payment of an Award with respect to any Plan Year
beginning on or after January 1, 2001 on the prior approval of a majority vote
of the shareholders of Cox.

6.       DESIGNATION OF BENEFICIARIES

         Each Participant may designate in writing and deliver to Cox the name
and address of the person or persons to whom an Award remaining payable under
this Plan shall be paid in the event of the Participant's death. If the
Participant has failed to make and deliver such a designation to Cox, or if no
person so designated survives the Participant, then Cox shall pay such an Award
to the Participant's lawful spouse, if then living, or, if not then living,
equally to the Participant's then living children, or, if none survive the
Participant, to the Participant's estate.

7.       LIMITATION ON CLAIM FOR BENEFITS

         Participants shall look solely to Cox for satisfaction of a claim for
an Award under this Plan. In no event shall the Board or any director, officer,
employee, or agent of Cox, including members of the Committee, be liable in its,
his or her individual capacity to any person whomsoever for the payment of a
benefit under this Plan. All payments under this Plan shall be made from Cox's
general assets, and no person under any circumstances whatsoever shall have a
claim for a benefit or payment under this Plan which is superior in any manner
whatsoever to an unsecured claim for a payment by a general creditor of Cox.

8.       WITHHOLDING ON BENEFIT PAYMENTS

         Notwithstanding any other provisions of the Plan, Cox shall be entitled
to withhold from each Award paid under this Plan such amounts as are required by
applicable state or Federal law or the order of any court.

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9.       NO ALIENATION, ASSIGNMENT OR OTHER RIGHTS

         Neither the Participant nor the person(s) designated as the
Participant's beneficiaries shall have any right whatsoever to alienate,
commute, anticipate or assign (either at law or in equity) all or any portion of
any Award payable under this Plan.

10.      GOVERNING LAW

         This Plan shall be interpreted under the laws of the State of Georgia,
to the extent not preempted by Federal law.

11.      SAVINGS CLAUSE

         If any provision of this Plan is held invalid or unenforceable, it will
not affect the other provisions. The Plan will remain in effect as though the
invalid or unenforceable provisions were omitted.

12.      AMENDMENT AND TERMINATION

         The Committee reserves the right to amend or terminate this Plan at any
time without the consent of the shareholders of Cox; except as required by any
federal or state law or by the rules of any stock exchange on which shares of
the common stock of Cox are listed. No such amendment or termination shall
retroactively reduce the amount of an Award already accrued to the benefit of
any Participant prior to the effective date of the amendment or the termination
of the Plan.

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