<PAGE>
 
                                                                    EXHIBIT 10.2
                                THIRD AMENDMENT
                                      TO
                           SECURED CREDIT AGREEMENT


          THIS THIRD AMENDMENT (this "Amendment") dated as of May 20, 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 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 and incurrence of Convertible Subordinated Debentures (the "2004
Subordinated Debt") due 2004 pursuant to the terms and conditions of a certain
Indenture to be dated on or near June 1, 1997 (substantially in the form
attached hereto as Exhibit A, the "Indenture") between the Borrower and Bankers
Trust Company, a banking corporation duly organized and existing under the laws
of the state of New York, as trustee;

          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 and incurrence of the 2004 Subordinated Debt.

          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:

          SECTION 1.  AMENDMENTS.
                      ---------- 

          Upon receipt of the documents to be delivered by the Borrower pursuant
to Section 2 below, and in reliance on the Borrower's warranties set forth in
Section 3 below, as of the date hereof the Credit Agreement shall be hereby
amended as follows:

          (a) Section 1.1 of the Credit Agreement is amended by revising the
     definition of "Subordinated Debt" to read in its entirety as follows:
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          "    "Subordinated Debt" means Debt of the Borrower (A) (1) which is
          subordinated in priority of payment to the Debt of the Borrower under
          this Agreement and the Revolving Note in a manner consistent with the
          BCI Subordination Agreement and (2) which shall not mature prior to
          the Termination Date (the Lenders acknowledge that, (a) prior to the
          conversion thereof into equity, the BCI Convertible Debt shall
          constitute "Subordinated Debt", and (b) any other Debt owed to BCI by
          the Borrower existing as of the Effective Date and covered by the
          terms and conditions of the BCI Subordination Agreement shall
          constitute "Subordinated Debt"), and (B) pursuant to the Convertible
          Subordinated Debentures (the "2004 Subordinated Debt") due 2004 issued
          pursuant to the terms and conditions of a certain Indenture (the "2004
          Indenture") dated on or near June 1, 1997 between the Borrower and
          Bankers Trust Company, a banking corporation duly organized and
          existing under the laws of the state of New York, as trustee."

          (b) Section 6.2 of the Credit Agreement is amended by deleting the
     "and" at the end of Section 6.2(12) of the Credit Agreement, redesignating
     Section 6.2(13) of the Credit Agreement as Section 6.2(14) of the Credit
     Agreement, and adding a new Section 6.2(13) of the Credit Agreement to read
     in its entirety as follows:

          "  (13)  2004 Subordinated Debt; and"

          (c) Section 6.14 of the Credit Agreement is amended to read in its
     entirety as follows:

          "    SECTION 6.14   Subordinated Debt.  Make any payment or prepayment
          with respect to any Subordinated Debt, except that (i) interest may be
          paid on Subordinated Debt to the extent permitted by the terms of such
          Subordinated Debt (including without limitation the BCI Subordination
          Agreement or the 2004 Indenture if applicable), including without
          limitation the subordination provisions thereof, and (ii) prior to an
          Event of Default, Subordinated Debt and interest thereon may be
          converted into equity of the Borrower or may be prepaid solely from
          the proceeds of a substantially contemporaneous issuance of equity or
          Subordinated Debt of the Borrower; provided, that within fifteen (15)
          Business Days of the receipt of any BCI Exempted Stock, the Borrower
          may prepay principal of the BCI Convertible Debt by an amount equal to
          the net cash proceeds received from the disposition of such BCI
          Exempted Stock."

                                      -2-
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          SECTION 2.  CERTAIN DOCUMENTS.
                      ----------------- 

          Concurrently herewith the Borrower has delivered the following to the
Agent, each duly executed and appropriately dated and in form and substance
satisfactory to the Agent:

          (a)  Certificate of the Borrower.  A certificate of the Secretary of
     the Borrower certifying (i) a true and correct copy of the most recent
     draft of the Indenture (it being understood that any changes to the
     Indenture must be approved by the Agent); (ii) a copy of the Certificate of
     Incorporation and bylaws of the Borrower (or a statement that no change has
     been made to such documents since the date of the Credit Agreement), and
     (iii) resolutions of the board of directors of the Borrower authorizing the
     execution, delivery and performance by the Borrower of the Indenture, the
     transactions contemplated thereby and the incurrence of the 2004
     Subordinated Debt.

          (b)  Legal Opinions.  A copy of all legal opinions delivered in
     connection with the Indenture on behalf of the Borrower together with
     reliance letter(s) relating thereto permitting the Lenders to rely on
     opinions as to the authorization of the issuance and incurrence of the 2004
     Subordinated Debt and other similar matters.

          (c)  Miscellaneous.  Such other approvals, opinions or documents as
               -------------                                                 
     the Agent may reasonably request.

          SECTION 3.  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 the Credit
     Agreement and Loan Documents 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.

          SECTION 4.  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.

                                      -3-
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          (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.

                                      -4-
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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 Di Donato
                                           ------------------------------
                                           Title:  Vice President
                                                 ------------------------


                                       LASALLE NATIONAL BANK


                                       By: /s/ John C. Thurston
                                           ------------------------------
                                           Title: Commercial Loan Officer
                                                 ------------------------


                                       HARRIS TRUST AND SAVINGS BANK


                                       By: /s/ John 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
                                           ------------------------------  

                                       BALTIMORE BAGEL CO.

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

                                      -5-
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                                       NOAH'S NEW YORK BAGELS, INC.

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

                                      -6-