<PAGE>
 
                               SECOND AMENDMENT
                                      TO
                           SECURED CREDIT AGREEMENT


          THIS SECOND AMENDMENT dated as of April 29, 1997 is entered into by 
and among Einstein/Noah Bagel Corp. (f/k/a Einstein Bros. Bagels, Inc.), a 
Delaware corporation (the "Borrower"), the lenders who are party to the Credit 
Agreement referred to below (the "Lenders") and Bank of America Illinois, an 
Illinois banking corporation, as Agent for the Lenders (herein, in such 
capacity, the "Agent").

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

          WHEREAS, the Borrower, the Lenders and the Agent are parties to a
certain Secured Credit Agreement dated as of May 17, 1996 (as heretofore
amended, called the "Credit Agreement"; terms used but not otherwise defined
herein are used herein as defined in the Credit Agreement);


          WHEREAS, the Borrower desires to amend the Credit Agreement to permit
the issuance, in certain circumstances, of Letters of Credit expiring after the
Termination Date without first pledging cash collateral; 


          WHEREAS, subject to the terms and conditions set forth herein the
Agent and the Lenders are willing to amend the Credit Agreement so as to, among
other things, permit the issuance of such Letters of Credit.


          NOW, THEREFORE, in consideration of the premises, and intending to be
legally bound hereby, the Borrower, the Agent and the Lenders hereby agree as
follows:


<PAGE>
 
          SECTION 1.  AMENDMENTS.
                      ----------

          In reliance on the Borrower's warranties set forth in Section 2 below,
as of the date hereof,

          (a)  Section 2.3A of the Credit Agreement is amended to read in its
     entirety as follows:

          "    Section 2.3A Expiration. Each Letter of Credit may expire before,
          on or after the Termination Date; provided, that with respect to each
          Letter of Credit expiring after the Termination Date, the Borrower
          hereby agrees to pledge cash collateral to the Agent, no later than
          thirty (30) days prior to the Termination Date, in an amount, and
          pursuant to documentation, reasonably satisfactory to the Issuing
          Lender and the Agent."

          (b)  Section 8.1(3) of the Credit Agreement is amended to read in its 
     entirety as follows:

          "The Borrower or any Subsidiary shall fail to perform or observe any
          term, covenant or agreement contained in Sections 2.3A, 6.3, 6.6,
          6.9, 6.10, 6.12, 6.13, and 6.14 of this Agreement applicable thereto;"

          SECTION 2.  WARRANTIES.
                      ----------

          To induce the Agent and the Lenders to enter into this Amendment, the 
Borrower warrants to the Agent and the Lenders as of the date hereof that:

          (a)  The representations and warranties contained in Article IV of the
     Credit Agreement are true and correct in all material respects on and as of
     the date hereof (except to the extent such representations and warranties
     expressly refer to an earlier date); and

          (b)  No Default or Event of Default has occurred and is continuing.


<PAGE>
 
          SECTION 3.  GENERAL.
                      -------

          (a)  As hereby modified, the Credit Agreement shall remain in full
     force and effect and is hereby ratified, approved and confirmed in all
     respects.

          (b)  This Amendment shall be binding upon and shall inure to the
     benefit of the Borrower, the Lenders and the Agent and respective
     successors and assigns of the Lenders and the Agent.

          (c)  This Amendment may be executed in any number of counterparts and
     by the different parties on separate counterparts, and each such
     counterpart shall be deemed to be an original, but all such counterparts
     shall together constitute but one and the same Amendment.
<PAGE>
 
Delivered at Chicago, Illinois, as of the date and year first above written.

                                        
                                         EINSTEIN/NOAH BAGEL CORP.


                                         By:  /s/ Paul A. Strasen
                                              -----------------------------
                                              Title: Senior Vice President
                                                     ----------------------



                                         BANK OF AMERICA ILLINOIS, as Agent


                                         By:  /s/ David A. Johanson
                                              -----------------------------
                                              Title: Vice President
                                                     ----------------------



                                         BANK OF AMERICA ILLINOIS, as Lender


                                         By:  /s/ L. Richard DiDonato
                                              -----------------------------
                                              Title: Vice President
                                                     ----------------------


                                         LASALLE NATIONAL BANK


                                         By:  /s/ Meg Marion
                                              -----------------------------
                                              Title: Senior Vice President
                                                     ----------------------


                                         HARRIS TRUST AND SAVINGS BANK


                                         By:  /s/ Jan M. Dillon    
                                              -----------------------------
                                              Title: Vice President
                                                     ----------------------


     The undersigned hereby acknowledge the foregoing amendments and reaffirm 
their respective duties and obligations arising under the Loan Documents to 
which each is a party.

                                         BRACKMAN BROTHERS, INC.


                                         By:  /s/ Paul A. Strasen
                                              -----------------------------
                                         Its: President
                                              -----------------------------

<PAGE>
 
                                        
                                         BALTIMORE BAGEL CO.


                                         By:  /s/ Paul A. Strasen
                                              -----------------------------
                                         Its: President
                                              -----------------------------


                                         NOAH'S NEW YORK BAGELS, INC.


                                         By:  /s/ Paul A. Strasen
                                              -----------------------------
                                         Its: President
                                              -----------------------------


                                         BRACKMAN BROTHERS OF IDAHO, INC.


                                         By:  /s/ Paul A. Strasen
                                              -----------------------------
                                         Its: Vice President
                                              -----------------------------