<PAGE>
 
                                                                    EXHIBIT 10.6


                        AMENDMENT TO CHANGE OF CONTROL
                              SEVERANCE AGREEMENT



          This Amendment to Change of Control Severance Agreement ("Amendment")
is entered into as of December 29, 1995, by and among BSB Bancorp, Inc. (the
"Corporation"), a Delaware corporation, its wholly-owned subsidiary BSB Bank &
Trust Company, as successor to Binghamton Savings Bank ("Employer"), and LARRY
G. DENNISTON, ("Executive").

                                 WITNESSETH:

          WHEREAS, the Corporation, Employer and Executive have heretofore
entered into a Change of Control Severance Agreement (the "Agreement") dated as
of November 2, 1990; and

          WHEREAS, the parties desire to amend the Agreement;

          NOW, THEREFORE, in consideration of the mutual covenants and promises
contained herein and in the Agreement, and other good and valuable
consideration, the receipt and adequacy of which is hereby acknowledged, the
parties agree as follows:

          1. A new Subsection (d) is added at the end of Section 2 of the
     Agreement, to read as follows:

          (d)    Notwithstanding any other provision of this Agreement or of any
     other agreement, contract, or understanding heretofore or hereafter entered
     into between Executive and the Corporation or Employer (or any subsidiary
     or affiliate of either of them), except an agreement, contract, or
     understanding hereafter entered into that expressly modifies or excludes
     application of this paragraph (the "Other Agreements"), and notwithstanding
     any formal or informal plan or other arrangement heretofore or hereafter
     adopted by the Corporation or Employer (or any subsidiary or affiliate of
     either of them) for the direct or indirect provision of compensation to
     Executive (including groups or classes of participants or beneficiaries of
     which Executive is a member), whether or not such compensation is deferred,
     is in cash, or is in the form of a benefit to or for Executive (a "Benefit
     Plan"), Executive shall not have any right to receive any payment or other
     benefit under this Agreement, any Other Agreement, or any Benefit Plan if
     such payment or benefit, taking into account all other payments or benefits
     to or for Executive under this


     Agreement, all Other Agreements, and all Benefit Plans, would cause any
     payment to Executive under this Agreement to be considered a "parachute
     payment" within the meaning of Section 28OG(b)(2) of the Internal Revenue
     Code of 1986, as amended (a "Parachute Payment").  In the event that the
     receipt of any such payment or benefit under this Agreement, any Other
     Agreement, or any Benefit Plan would cause Executive to be considered to
     have received a Parachute Payment under this Agreement, then Executive
     shall have the right, in Executive's sole discretion, to designate those
     payments or benefits under this Agreement, any Other Agreements, and/or any
     Benefit Plans, which should be reduced or eliminated so as to avoid having
     the payment to Executive under this Agreement be deemed to be a Parachute
     Payment.

          2. References in the Agreement to "Binghamton Savings Bank" shall be
     deemed to be references to "BSB Bank & Trust Company."
<PAGE>
 
          3. In all other respects, the Agreement shall continue in full force
     and effect.

     IN WITNESS WHEREOF, Executive has hereunto set his hand, and the
Corporation and Employer have caused this Amendment to be executed in their
names and on their behalves, all as of the day and year first above written.

                                    BSB BANCORP, INC.


ATTEST:  Cynthia A. Hicks           By:  William H. Rincker
         ----------------                ------------------
         (Assistant Secretary)           (Chief Executive Officer)

                                    BSB BANK & TRUST COMPANY


ATTEST:  Cynthia A. Hicks           By:  William H. Rincker
         ----------------                ------------------
         (Assistant Secretary)           (Chief Executive Officer)

                                    EXECUTIVE



                                    Larry G. Denniston
                                    -------------------------
                                    Larry G. Denniston


                                 -2-