<PAGE>   1
                                                                   Exhibit 10(q)

[The Gillette Company LOGO]



May 27, 1999

Mr. Alfred M. Zeien
4900 Prudential Tower Building
Boston, MA 02199

Re: ESTATE PRESERVATION PLAN II
    ---------------------------

Dear Al:

Pursuant to resolutions adopted by this Company's Board of Directors at its
April 15, 1999 meeting, I am please to extend this offer to you, under the terms
and conditions described below, to purchase a life insurance policy with a death
benefit payable following the deaths of both Joyce and you.

Under this arrangement, the Company will agree to make stated payments to an
insurance company over a five-year period in order to fund the annual premium
cost of the death benefit coverage under the policy. The Company's cumulative
payments will be returned to the Company, without interest, at the end of the
fifteenth (15th) policy year or, if sooner occurring, following the deaths of
Joyce and you. The trust designated as the owner of the policy will be
responsible for the annual cost of the life insurance protection as well as any
additional cost of the insurance coverage following the 15th policy year. As a
condition to the issuance of the policy, you and the policyowner will execute a
Split-Dollar Agreement and Collateral-Assignment (in the forms annexed hereto)
which documents shall establish the respective rights of the Company and the
policyowner with respect to the death benefit proceeds and cash value (including
investment direction, loans and withdrawals) under the policy. Other terms and
conditions of this life insurance arrangement are set forth on the Term Sheet
annexed hereto.

In consideration of the aforementioned life insurance arrangement, you agree to
forego and waive irrevocably your right to any benefits otherwise payable under
the Company's Supplemental Savings Plan. Your waiver of these benefits will
result in certain cash and financial cost savings to the Company, from which
savings the Company will obtain the funding for the purchase of the life
insurance policy. For the purposes of determining the amount of life insurance
coverage to be purchased, the value of your benefit under the Company's
Supplemental Savings Plan will been calculated as of the close of the business
day today and increased by the amount that otherwise would be credited to your


<PAGE>   2


                                      -2-


Supplemental Savings Plan accounts (without earnings), at your current savings
contribution and salary rates, until your retirement date.

By signing where indicated below, you accept this offer and signify your
agreement to forego and waive irrevocably the Supplemental Savings Plan benefits
specified above, to have executed the Split-Dollar Agreement,
Collateral-Assignment and such other documents as may be necessary or desirable
to implement your coverage under the life insurance policy, and to do such
further actions (including a medical examination for underwriting purposes) as
may be necessary or desirable to effectuate the purposes of this arrangement.
Joyce also must sign below agreeing to the above-described actions related to
the purchase of the life insurance policy.

You are further acknowledging that there are certain tax considerations to be
evaluated in accepting this offer and that you have had the opportunity to
review these tax issues with your personal tax advisor before accepting this
offer. You agree to be fully responsible for the tax consequences of your
participation in this arrangement, and acknowledge that the Company reserves the
right to seek reimbursement from you if the Company is charged with the
obligation to pay any of your income or employment taxes in respect of this
arrangement.

This arrangement may be modified only by written agreement between you and an
authorized representative of the Company. This arrangement shall inure to the
benefit of, and shall be binding upon, you and your heirs, personal
representatives, successors and assignees, and upon the Company and its
officers, directors, employees, shareholders and their successors and assignees.

This arrangement shall be construed and enforced under the laws of the
Commonwealth of Massachusetts.

Please return one copy of this letter, signed where indicated below, to indicate
your agreement to the foregoing terms by the close of the business day on June
4, 1999.


Very truly yours,


/s/ Robert E. DiCenso

Robert E. DiCenso
Senior Vice President - Personnel and Administration



<PAGE>   3


                                      -3-



ACCEPTANCE OF OFFER:

I hereby accept the Company's offer and agree to the terms and conditions of the
arrangement set forth above and contained in the documents annexed hereto.



/s/ Alfred M. Zeien
-----------------------------
Alfred M. Zeien



/s/ Joyce Zeien
-----------------------------
Joyce Zeien