<PAGE>
 
                                                                   Exhibit 10.15

                           SECOND AMENDMENT AGREEMENT
                           --------------------------

           SECOND AMENDMENT AGREEMENT (this "Amendment Agreement") dated as of
December 27, 1996 by and among Moore Medical Corp. (the "Borrower"), Bank of
Boston Connecticut and certain other lending institutions (collectively, the
Banks"), and Bank of Boston Connecticut, as agent for the Banks (in such
capacity, the "Agent"), amending a certain Revolving Credit Agreement dated as
of January 9, 1996, as amended by the First Amendment Agreement dated as of
March 1, 1996 (as amended, the "Credit Agreement").

                                   WITNESSETH
                                   ----------

           WHEREAS, the Borrower has requested, among other things, that the
Agent and the Banks amend certain terms and conditions of the Credit Agreement;
and

           WHEREAS, the Agent and the Banks are willing to amend certain terms
and conditions of the Credit Agreement on the terms and conditions set forth
herein.

           NOW, THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto agree as
follows:

           (S)1.  Definitions.  Capitalized terms used herein without definition
                  -----------
that are defined in the Credit Agreement shall have the same meanings herein as
therein.

           (S)2.  Ratification of Existing Agreements. All of the Borrower's
                  ------------ -- -------- ----------
obligations and liabilities to the Agent and the Banks, and all the Agent's and
Banks' obligations and liabilities to the Borrower, as evidenced by or otherwise
arising under the Credit Agreement, the Notes and the other Loan Documents
except as otherwise expressly modified in this Amendment Agreement upon the
terms set forth herein, are, by the Borrower's, the Agent's and Banks',
execution of this Amendment Agreement ratified and confirmed in all respects. In
addition, by the Borrower's execution of this Amendment Agreement, the Borrower
represents and warrants that, subject to provided and provided, however, clauses
                                         --------     --------  -------
of Section 5.4 of the Credit Agreement, no counterclaim, right of set-off or
defense of any kind exists or is outstanding with respect to such obligations
and liabilities.

           (S)3.  Representations and Warranties. All of the representations
                  --------------- --- ----------
and warranties made by the Borrower in the Credit Agreement, the Notes and the
other Loan Documents are true and correct on the date hereof as if made on and
as of the date hereof, except to the extent that any of such representations and
warranties relate by their terms to a prior date and except to the extent of
changes resulting from transactions contemplated or permitted by the Credit
Agreement and changes occurring in the ordinary course of business that singly
or in the aggregate do not have a Material Adverse Effect.
<PAGE>
 
(S)4.   Conditions Precedent.  The effectiveness of the amendments contemplated
        ---------- ---------
hereby shall be subject to the satisfaction on or before the date hereof of each
of the following conditions precedent:

                     (a)     Representations and Warranties. All of the
                             ------------------------------
        representations and warranties made by the Borrower herein, whether
        directly or incorporated by reference, shall be true and correct on the
        date hereof, except as provided in (S)3 hereof.

                     (b)     Performance; No Event of Default.  The Borrower
                             --------------------------------
        shall have performed and complied in all material respects with all
        terms and conditions herein required to be performed or complied with by
        it prior to or at the time hereof, and there shall exist no Default or
        Event of Default.

                     (c)     Corporate Action.  All requisite corporate action
                             ----------------
        necessary for the valid execution, delivery and performance by the
        Borrower of this Amendment Agreement and all other instruments and
        documents delivered by the Borrower in connection therewith shall have
        been duly and effectively taken.

                     (d)     Delivery.  The parties hereto shall have executed
                             --------
        and delivered this Amendment Agreement. In addition, the Borrower shall
        have executed and delivered such further instruments, and take such
        further action as the Agent and the Banks may have reasonably requested,
        in each case further to effect the purposes of this Amendment Agreement,
        the Credit Agreement and the other Loan Documents.

                     (e)     Fees and Expenses.  The Borrower shall have paid to
                             -----------------
        the Banks all fees and expenses incurred by the Agent in connection with
        this Amendment Agreement, the Credit Agreement or the other Loan
        Documents on or prior to the date hereof.

                     (f)     Assignments.  Each of Bank of Scotland and Fleet
                             -----------
        National Bank of Connecticut shall have assigned all of their right,
        title and interest under the Credit Agreement and the other Loan
        Documents pursuant to an Assignment and Acceptance executed and
        delivered by each of Bank of Scotland and Fleet National Bank of
        Connecticut and Bank of Boston Connecticut. In addition, each of Bank of
        Scotland and Fleet National Bank of Connecticut shall have (i) returned
        to the Agent their respective Revolving Credit Notes marked "canceled"
        and (ii) received payment of all amounts due and payable to each of them
        under the Credit Agreement as of the date hereof.

        (S)5.  Amendments to the Credit Agreement.
               ---------- ------ ------ ---------

                     (S)5.1. Amendment to (S)5.2.  Section 5.2 of the Credit
                             --------- -- ------
        Agreement is hereby amended in its entirety to read as follows:

                     "(S)5.2.[Intentionally Omitted]."
<PAGE>
 
                     (S)5.2. Amendment to (S)10.4.  Section 10.4 of the Credit
                             --------- -- -------
        Agreement is hereby amended in its entirety to read as follows:

                             "(S)10.4 The Borrower will not permit Consolidated
                             Tangible Net Worth to be less than the sum of
                             $25,500,000, plus on a cumulative basis, fifty
                                          ----
                             percent (50%) of positive Consolidated Net Income
                             for each fiscal year of the Borrower ending after
                             December 28, 1996."

                     (S)5.3. Amendment to (S)1.  Schedule 1 to the Credit
                             --------- -- ----   -------- -
        Agreement is hereby deleted in its entirety and Schedule 1 attached
                                                        -------- -
        hereto is hereby substituted therefor.

                     (S)5.4. Amendment to Borrowing Base.  The definition of
                             --------- -- --------- ----
        "Borrowing Base" appearing in Schedule 2 to the Credit Amendment is
                                      -------- -
        hereby amended by deleting the number "$33,000,000" appearing in
        subsection (b) (ii) of such definition and substituting therefor the
        number "$25,000,000".

                     (S)5.5. Amendment to Revolving Credit Loan Maturity Date.
                             --------- -- --------- ------ ---- -------- ----
        The definition of "Revolving Credit Loan Maturity Date" appearing in
        Schedule 2 to the Credit Agreement is hereby amended by deleting the
        -------- -
        date "December 31, 1998" appearing therein and substituting therefor the
        date "December 31, 1999".

        (S)6.        Expenses.  The Borrower agrees to pay to the Agent upon
                     --------
demand an amount equal to any and all out-of-pocket costs or expenses (including
reasonable legal fees and disbursements and appraisal expenses) incurred or
sustained by the Agent in connection with the preparation of this Amendment
Agreement and any related matters.

        (S)7.        Miscellaneous.
                     -------------

                     (a)   This Amendment Agreement shall be governed by and
        construed in accordance with the laws of the State of Connecticut.

                     (b)   Except as otherwise expressly provided by this
        Amendment Agreement, all of the respective terms, conditions and
        provisions of the Credit Agreement shall remain the same. It is declared
        and agreed by each of the parties hereto that the Credit Agreement, as
        amended hereby, shall continue in full force and effect, and that this
        Amendment Agreement and the Credit Agreement be read and construed as
        one instrument, and all references in the Loan Documents to the Credit
        Agreement shall hereafter refer to the Credit Agreement, as amended by
        this Amendment Agreement.
<PAGE>
 
           IN WITNESS WHEREOF, each of the parties hereto have caused this
Agreement to be executed in its name and behalf by its duly authorized officer
as of the date first written above.

                                        MOORE MEDICAL CORP.

                                        
                                        By: /s/ John A. Murray
                                           ----------------------------- 
                                        Title:  Vice President
                                        


                                        BANK OF BOSTON CONNECTICUT,
                                        Individually and as Agent
                                        

                                        By: /s/ Donald W. Peters
                                           ----------------------------- 
                                        Title:  Vice President
                                        


                                        FLEET BANK, N.A.

                                        
                                        By: /s/ Jeff J. White
                                           ----------------------------- 
                                        Title:  Vice President
                                        


                                        BANK OF SCOTLAND

                                        
                                        By: /s/ Elizabeth Wilson
                                           ----------------------------- 
                                        Title:  Vice President
                                                and Branch Manager
<PAGE>
 
                                   SCHEDULE 1
                                   ----------

                                       TO
                                       --

                           REVOLVING CREDIT AGREEMENT
                           --------------------------

<TABLE> 
<CAPTION> 

-----------------------------------------------------------------------------------------------
                  BANK                           COMMITMENT                    COMMITMENT      
                  ----                           ----------                    ----------      
                                                 PERCENTAGE                                    
                                                 ----------
-----------------------------------------------------------------------------------------------
<S>                                              <C>                           <C> 
Bank of Boston Connecticut                        100.00%                      $35,000,000      
81 West Main Street                                                                            
Waterbury, Connecticut 06702                                                                   
Attn:  Donald Peters,                                                                          
Vice President                                                                                 
Telephone:   (203) 575-3733                                                                    
Telecopy:    (203) 574-7599                                                                    
-----------------------------------------------------------------------------------------------
TOTAL COMMITMENT                                    100%                       $35,000,000
----------------                                    ----
-----------------------------------------------------------------------------------------------
</TABLE>