<PAGE>   1
                                                                    Exhibit 10.2

                                 AMENDMENT NO. 1
                                       TO
                     ESOP STOCK SALE AND EXCHANGE AGREEMENT


         This AMENDMENT NO. 1 TO THE ESOP STOCK SALE AND EXCHANGE AGREEMENT is
dated as of September 25, 1998 by and among SIMMONS HOLDINGS, INC., a Delaware
corporation ("Holdings"), SIMMONS COMPANY, a Delaware corporation (the
"Company"), STATE STREET BANK & TRUST COMPANY, solely in its capacity as Trustee
(the "Trustee") of the Simmons Company Employee Stock Ownership Trust (the
"ESOT") and REM Acquisition, Inc., a Delaware corporation ("MergerCo").

                              W I T N E S S E T H:
                              --------------------

         WHEREAS, Holdings, the Company, the Trustee and MergerCo are parties to
the ESOP Stock Sale and Exchange Agreement dated as of July 22, 1998 (the "ESOP
Agreement"); and

         WHEREAS, such parties desire to amend the ESOP Agreement as set forth
herein; and

         WHEREAS, terms defined in the ESOP Agreement and not otherwise defined
herein are used with the meanings so defined;

         NOW THEREFORE, in consideration of the mutual agreements set forth
herein the parties hereto do hereby agree as follows:

         1. All references to "Agreement" in the ESOP Agreement shall refer to
the ESOP Agreement as amended from time to time.

         2. Section 1.1 of the ESOP Agreement is hereby amended such that the
phrase "for a purchase price per share in cash of $7.1463" shall instead read
"for a purchase price per share in cash of $6.8663."

         3. Section 2.1 of the ESOP Agreement is hereby amended such that the
phrase "Holdings shall issue to the Trustee in exchange therefore an aggregate
of 3,484,997 shares of Class C Stock of Holdings" shall instead read "Holdings
shall issue to the Trustee in exchange therefore an aggregate of 3,482,036
shares of Class C Stock of Holdings."






                                       -1-


<PAGE>   2



         4. Section 4.4 of the ESOP Agreement is hereby amended and restated in
its entirety to read as follows:

         "Section 4.4 FAIRNESS OPINION. On September 24, 1998, the ESOT has
received the fairness opinion (the "ESOT Fairness Opinion") of HL to the effect
that the consideration to be received by the ESOT for the ESOP Shares in
connection with the transactions contemplated by this Agreement and the Merger
is not less than fair value and that such transactions, considered as a whole,
is fair to the ESOP from a financial point of view, and such opinion has not
been withdrawn, qualified or otherwise modified."

         5. Section 5.5 is hereby amended such that the phrase "commitment
letters (the"Commitment Letters") relating to the provisions of such financing"
shall instead read "the commitment letters (the "Commitment Letters") dated
September 22, 1998, true and complete copies of which were provided to the
Trustee on September 23, 1998, relating to the provisions of such financing."

         6. Section 8.1.5(b) is hereby amended such that the phrase "in the
Commitment Letters and the pro forma information delivered to the Trustee on
July 20, 1998" shall instead read "in the Commitment Letters and the pro forma
information delivered to the Trustee on September 23, 1998."

         7. The Trustee, by its execution hereof, hereby consents pursuant to
Section 8.1.5(c) of the ESOP Agreement to Amendment No. 1 to the Agreement and
Plan of Merger dated as of September 22, 1998 and hereby agrees pursuant to
Section 10.2 to extend the term of the ESOP Agreement to October 30, 1998.

         8. This Amendment shall be effective immediately. As modified hereby,
the ESOP Agreement remains in full force and effect in all respects.


                                       -2-


<PAGE>   3



         IN WITNESS WHEREOF, the parties have caused this Amendment to be
executed as of the day and year first above written.

SIMMONS HOLDINGS, INC., a Delaware corporation


By:   /s/ Zenon S. Nie
   ---------------------------------------
          Name: Zenon S. Nie
          Title:  Chief Executive Officer


SIMMONS COMPANY, a Delaware corporation


By:   /s/ Zenon S. Nie
   ---------------------------------------
          Name: Zenon S. Nie
          Title:  Chief Executive Officer

STATE STREET BANK AND TRUST COMPANY,
AS TRUSTEE OF THE SIMMONS COMPANY EMPLOYEE
STOCK OWNERSHIP TRUST


By:   /s/ Kelly Q. Driscoll
   ---------------------------------------
      Name: Kelly Q. Driscoll
      Title: Vice President

REM ACQUISITION, INC., a Delaware corporation


By:   /s/ Gregory P. Meredith
   ---------------------------------------
       Name: Gregory P. Meredith
       Title: Vice President







                                       -3-