<PAGE>
 
                                                                    EXHIBIT 10.5

                              SECOND AMENDMENT TO
                             AMENDED AND RESTATED
                      COMPUTER AND COMMUNICATIONS SYSTEMS
                              SERVICES AGREEMENT


          This Second Amendment to Computer and Communications Systems Services
Agreement ("Second Amendment") is made and entered into this 25/th/ day of June,
1998 by and between Einstein/Noah Bagel Corp., a Delaware corporation (the
"Company"), and Boston Chicken, Inc., a Delaware corporation ("BCI").


                                   RECITALS
                                   --------

          The Company and BCI are parties to an amended and restated computer
and communications systems services agreement dated May 28, 1996, as amended
(the "Services Agreement").  The parties now desire to amend the Services
Agreement as hereafter set forth.


                                   COVENANTS
                                   ---------

          In consideration of the matters recited above and the mutual covenants
of the parties, the parties hereto agree as follows:

          1.1  Amendment. The Services Agreement shall be amended as of the date
               ---------                                  
hereof as follows:

               (a) The Services Agreement is amended by changing "Einstein Bros.
          Bagels, Inc." to "Einstein/Noah Bagel Corp." and "EBBI" to "ENBC" each
          place where such terms appear.

               (b) Section 3.B of the Services Agreement is hereby amended by
          adding the following sentence at the end of the first sentence
          thereof:

               "ENBC has, as of the date of this Second Amendment, closed 
               thirty-five ENBC Units with respect to each of which ENBC has
               paid a Licensed Program Fee. From and after the date hereof, the
               Licensed Program Fee paid for each such closed ENBC Unit shall be
               transferred to and applied against the Licensed Program Fee due
               for the next thirty-five successive new ENBC Units opened by ENBC
               or its licensees, except to the extent BCI is obligated to pay
               amounts to third party software licensors with respect to such
               new units."

               (c) Section 3.C of the Services Agreement is hereby amended by
     deleting such section in its entirety and substituting therefor the
     following:
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          "3.C. DATA CENTER, NETWORK SERVICE AND SOFTWARE SUPPORT FEES

          (1) ENBC agrees to pay to BCI, for ongoing Data Center and Network
          Service Operations and support of the Infrastructure Programs, and for
          software support service, a fee per four or five week accounting
          period of BCI ("Accounting Period"), which shall be determined for
          fiscal 1998 by taking the "ENBC Portion" of fees for Systems for 1998,
          as shown on Exhibit B hereof, deducting therefrom fees previously paid
          by ENBC hereunder for fiscal 1998 and dividing the balance by the
          number of Accounting Periods remaining in fiscal 1998 for which ENBC
          has not yet made payment. Such fee shall be determined for Accounting
          Periods after fiscal 1998 by taking the "ENBC Portion" of fees for
          Systems for the applicable fiscal year (as set forth on a revised
          Exhibit B prepared by BCI, based on its budget for such fiscal year,
          in the same manner as Exhibit B hereof) and dividing such amount by
          13. All such fees shall be subject to adjustment as provided in
          Section 3.C(2) hereof.

          (2) To the extent BCI's actual overhead for its systems department
          (including, without limitation, any salary bonus, severance or other
          compensation paid to employees assigned to such department but
          excluding severance paid to employees terminated prior to fiscal 1998)
          for any fiscal quarter is greater or less than the applicable
          proportion of the amount shown on Exhibit B for such category of
          overhead, then the fees payable pursuant to Section 3.C(1) hereof for
          such fiscal quarter shall be recomputed, in the manner provided in
          Section 3.C(1), and any difference shall be paid to the party entitled
          thereto in three equal increments over the three Accounting Periods
          following the fiscal quarter for which such adjustment is made. BCI
          agrees to give ENBC upon ENBC's request all information reasonably
          requested by ENBC regarding the amounts BCI has budgeted or incurred
          for the foregoing overhead categories."

          (d) Section 3.D of the Services Agreement is hereby amended by
deleting the last sentence thereof.

          (e) Section 3.E of the Services Agreement is hereby deleted, and
Sections 3.F and 3.G are relettered Sections 3.E and 3.F, respectively.

          (f) The first paragraph of Section 7 of the Services Agreement is
hereby amended by deleting such paragraph in its entirety and substituting
therefor the following:

          "The term of this Agreement shall expire on March 26, 2000, unless the
          parties mutually agree to extend such term; provided that either party
          may terminate this Agreement on not less than six months' prior
          written notice;
     

                                       2
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          and provided further that BCI may terminate this Agreement without
          notice and cease rendering the services hereunder 15 days after notice
          of any non-payment of the fees and expenses provided for herein when
          such fees and expenses are due and payable, unless such non-payment is
          cured within such 15 day period. In connection with any termination of
          this Agreement (except where termination is based on ENBC's non-
          payment of fees and expenses), BCI agrees to provide to ENBC, at
          ENBC's expense, all assistance that may be reasonably requested by
          ENBC to assist ENBC in effecting a smooth and orderly transition from
          the provision of services hereunder by BCI to the provision of such
          services by ENBC employees or other service providers."

     2.1  Third Party Software. BCI represents and warrants that it has
          --------------------                                          
furnished ENBC true and correct copies of all third-party software licenses for
software made available to ENBC hereunder and that ENBC has the right to use all
such software made available to it without any liability or obligation by ENBC
to any such third-party.

     3.1  Continuing Effect of Services Agreement. The Services Agreement, as
          ---------------------------------------                          
amended hereby, is ratified and confirmed and remains in full force and effect.

     4.1  GOVERNING LAW. THIS SECOND AMENDMENT SHALL BE CONSTRUED IN ACCORDANCE
          -------------                                              
WITH AND GOVERNED BY THE LAWS OF THE STATE OF COLORADO APPLICABLE TO CONTRACTS
MADE AND TO BE PERFORMED THEREIN WITHOUT REGARD TO THE CONFLICTS OF LAW
PROVISIONS THEREOF.

     5.1  Counterparts. This Second Amendment may be executed in counterparts,
          ------------                                           
each of which shall be deemed an original, but each of which together shall
constitute but one and the same instrument.

     6.1  Headings. The headings of the sections of the Second Amendment are
          --------                                                       
inserted for convenience only and shall not be deemed to constitute a part of
this Second Amendment.


     IN WITNESS WHEREOF, the parties have executed this Second Amendment to be
effective on the date provided herein.


BOSTON CHICKEN, INC.                EINSTEIN/NOAH BAGEL CORP.


By:  /s/ Michael R. Daigle          By:  /s/ Paul A. Strasen
     -------------------------           ----------------------
Its: Senior Vice President and      Its: Senior Vice President
     -------------------------           ----------------------
     General Counsel
     -------------------------

                                       3
<PAGE>
 
1998 ENBC/BCI Fees
ENBC Fee calculation
--------------------
Exhibit B

<TABLE> 
<CAPTION> 
        Allocation Factors                                                             ENBC Fee Calculation
------------------------------------      ------------------------------------------------------------------------------------------
                                                                                                      Basis for             ENBC
Number of Stores                                                                       1998 Budget   Allocation  Factor    Portion
----------------                                                                       -----------   ----------  ------    -------
<S>                         <C>           <C>                                          <C>           <C>         <C>      <C> 
  Number of BM Stores         1,150   % ^                                          
  Number of ENBC Stores         550   % ^ Systems                                      $12,080,000   # Stores     32%     $3,908,235
                            -------                                                 
                              1,700%                                                
                                          Accounting                                   $ 2,658,252   # Stores     32%     $  6?0,023
  Number of People  (12/31/97)                                                                                  
  Number of BM People              % ^    Payroll & Admin. (Including Teleservices)    $ 2,594,395   # Stores     31%     $  804,262
  Number of ENBC People          31%                                                  
                            -------                                                 
                                100%      PeopleSoft Project Set-up (less Hardware)*   $ 2,016,716     Half       50%     $1,008,359
                                                                                    
                                          PeopleSoft Project Hardware                  $   470,000   # People     31%     $  146,700
                                                                                    
                                                                                       -----------                        ----------
                                          Total BCI Budget                             $19,619,365                        $6,726,579
</TABLE> 

*BCI shall include $939,236 of its PeopleSoft Development Cost in its 1999 
budget and $704,427 of its PeopleSoft Development Cost in its 2000 budget. Such
amounts represents financed project costs payable by BCI after 1998, and shall 
be allocated 50% to ENBC. In the event the agreement is terminated prior to 
the time ENBC's share of such amounts has been recovered by BCI, then ENBC shall
pay the remaining amounts to BCI at a rate of $117,405 per fiscal quarter. BCI 
agrees to take all actions required under its agreement with PeopleSoft, Inc. to
assure that ENBC shall not have any obligation to PeopleSoft to pay license 
fees for Peoplesoft software provided to ENBC hereunder, including without 
limitation executing and delivering appropriate assignment documents under 
Section 13 of such agreement.