<PAGE>

                                                    Exhibit (10)-34
                                                    Commonwealth Edison Company
                                                    Form 10-K File No. 1-1839



                               AMENDMENT NO. TWO
                                       TO
                              COMMONWEALTH EDISON
                          EXCESS BENEFIT SAVINGS PLAN
                          ---------------------------


          WHEREAS, Commonwealth Edison Company, an Illinois corporation (the
"Company"), has heretofore adopted and maintains a non-qualified deferred
compensation plan for the benefit of its employees and employees of certain of
its subsidiaries designated the Commonwealth Edison Company Excess Benefit
Savings Plan (the "Plan"); and

          WHEREAS, the Company desires to amend the Plan in certain respects.

          NOW, THEREFORE, pursuant to the power of amendment contained in
paragraph 8 of the Plan, the Plan is hereby amended, effective September 1,
1997, as follows:

     1.  Paragraph 3 is amended by adding the following new sentence at the end
     thereof:

<PAGE>

          Each Account shall be divided into a separate subaccount with respect
          to each earnings election made by a Participant pursuant to paragraph
          4 below.

     2.   Section 4 is hereby amended in its entirety to read as follows:

          4.  Earnings Elections.  The Committee shall from time to time
          designate two or more investment benchmarks, the rates of return or
          loss of which, based upon a Participant's earnings election, shall be
          used to determine the rate of return or loss to be credited to the
          subaccounts established within the Participant's Account pursuant to
          this paragraph 4. A Participant's earnings election shall specify the
          percentages of the Participant's Account allocated to the subaccounts
          with respect to each investment benchmark selected by the Participant,
          in increments of 5% (or multiples thereof). A Participant may change
          his or her earnings election as of the first business day of any
          calendar month by delivering to the Participant's Employer, at such
          time as may be specified by the Committee, a revised earnings
          election. A revised earnings election may apply to the then balance of
          a Participant's Account, to the future amounts to be credited thereto
          on account of the Participant's election under paragraph 2 of this
          Plan or both. If for any period of

                                      -2-
<PAGE>

          time an earnings election is not in effect pursuant to this paragraph
          4, the Participant's Account shall be credited with interest on the
          balance thereof as of the end of each calendar month at an annual rate
          equal to the imbedded rate of interest then being accrued by the
          Company on its long-term debt, as determined from time to time by the
          Comptroller of the Company.

     3.   Paragraph 6 is amended to read as follows:

          6.  Distribution.  Distribution of the balance of a Participant's
          Account shall be made at the time and in the manner specified below.

               (a) Retirement or Disability. If a Participant's employment
               terminates under circumstances entitling the Participant to a
               normal or early retirement pension under the Commonwealth Edison
               Company Service Annuity System or on account of the Participant's
               "disability" as defined therein, and as of the date of such
               termination the balance of the Participant's Account is at least
               $25,000, the balance of the Participant's Account shall be
               distributed to the Participant in installments, payable on or
               about the first day of each calendar quarter commencing with the
               first calendar quarter beginning after the date on which the

                                      -3-
<PAGE>

               Participant's employment terminates and continuing for fifteen
               years (the "Installment Period"). The amount of each installment
               payment shall be determined:

               (i) for the year in which installment payments are to commence,
               by dividing the balance of the Participant's Account as of the
               last day of the calendar quarter during which the Participant's
               employment terminates by the total number of payments to be made
               in the Installment Period;

               (ii) except as provided in clause (iii) below, for each
               subsequent calendar year, by dividing the balance of the
               Participant's Account as of September 30 (but subtracting from
               such balance the amount of the installment payment to be made on
               the next following October 1) by the total number of payments
               remaining to be made in the Installment Period (excluding the
               installment payment to be made on the next following October 1);
               and

               (iii) for the final calendar year in which installment payments
               are to be made, by dividing the balance of the Participant's
               Account as of the payment date by the number of payments
               remaining to be made in the Installment Period (including the
               installment payment which is then being made);

               provided, however, (I) if an installment payment calculated under
               subparagraph (i) above is to commence on October 1, such
               installments shall continue until the second succeeding January
               1, (II) no installment shall exceed the balance of the
               Participant's Account immediately before the date of payment and
               (III) the final installment shall be equal to the then remaining
               balance of

                                      -4-
<PAGE>

               the Participant's Account. Notwithstanding the foregoing, a
               Participant entitled to distribution under the first sentence of
               this paragraph 6(a) may elect to have such installments payable
               over ten years or five years, computed in the manner described in
               the preceding sentence, or to have the balance of his or her
               Account distributed in a single lump sum as of the first day of
               the calendar quarter next following the date the Participant's
               employment terminates, provided that such election is made at
               least one year prior to the date the Participant's employment
               terminates and provided further that in the case of a Participant
               who retires on or before September 1, 1998 and whose Account has
               not been distributed on or before August 1, 1997, such election
               may be made within 30 days after such Participant's termination
               of employment but shall not become effective until the first day
               of the calendar year that begins at least twelve months after
               such election.

               (b)  Distributions in the Event of Death. If a Participant's
               employment is terminated on account of the Participant's death,
               the balance of the Participant's Account shall be distributed to
               the

                                      -5-
<PAGE>

               Participant's beneficiary determined pursuant to paragraph 7 in a
               single lump sum as soon as is practicable following the end of
               the first calendar quarter coinciding with or next following the
               Participant's death. If a Participant dies after installment
               distributions have begun pursuant to paragraph 6(a), such
               installment distributions shall continue to the Participant's
               beneficiary determined pursuant to paragraph 7.

               (c) Other Distributions.  If a Participant's employment shall
               terminate for any reason other than those described in paragraph
               6(a) and (b), or if as of the date of a Participant's termination
               of employment the balance of the Participant's Account is less
               than $25,000, the balance of the Participant's Account shall be
               distributed to the Participant in a lump sum as soon as is
               practicable after the last day of the calendar quarter coinciding
               with or next following such termination of employment.

               (d) The amount of any distribution pursuant to this paragraph 6
               shall be reduced by any amount required by law to be deducted or
               withheld, including income tax withholding.



                                      -6-
<PAGE>

     IN WITNESS WHEREOF, the Company has caused this instrument to be executed
on this ____ day of ____________, 1997.


                              COMMONWEALTH EDISON COMPANY

                              By
                                 ---------------------------
                              Title
                                    ------------------------

ATTEST:


------------------------------

Title
      ------------------------


                                      -7-