EXHIBIT 10.4


                                  [LETTERHEAD]



                                              PERSONAL AND CONFIDENTIAL


May 28, 1996


Mid-Peninsula Bancorp
420 Cowper Street
Palo Alto, CA 94301

Attention:   Mr. David L. Kalkbrenner
             President & Chief Executive Officer

Dear David:

1.   This letter is to confirm our understanding that Mid-Peninsula Bancorp 
     ("Mid-Peninsula" or the "Company") or any successor corporation has 
     retained Alex. Brown & Sons Incorporated ("Alex. Brown") to act as 
     Mid-Peninsula's financial advisor and to assist Mid-Peninsula in 
     assessing the impact of, and the opportunities created by, the changing 
     environment among financial institutions. In this capacity, Alex. Brown 
     will provide financial advice to you as you deem necessary and analyze 
     alternative strategies, including acquisitions, mergers or other forms 
     of business combinations involving Mid-Peninsula. Specifically, Alex. 
     Brown will render the following general advisory services to the 
     Company:
     
     - Evaluation and complete financial analysis of acquisition 
       opportunities including, but not limited to, acquisitions of commercial 
       banks, thrift institutions, individual branches and non-depository 
       institutions.

     - Development of an acquisition strategy for Mid-Peninsula, including 
       assistance on such matters as the development of approach tactics to 
       each target institution, valuation, pro forma financial modeling and 
       analysis, negotiations, reviewing the financing alternatives for each 
       transaction and assistance in the handling of investor relations.

     - A full review of Mid-Peninsula's takeover defense posture, including 
       an analysis of the Company's existing defensive measures and 
       recommendation of additional actions if required.  A detailed review
       of the overall merger and acquisition


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Mid-Peninsula Bancorp
May 28, 1996
Page 2



       environment would also be presented with a particular emphasis 
       on (i) the strategies of the active acquirers within Mid-Peninsula's 
       trade area (ii) unsolicited offers for control; and (iii) the 
       actions undertaken unilaterally by shareholders to disrupt the 
       implementation of corporate strategy.

     - Active takeover defense assistance and strategic advice to Mid-
       Peninsula in the event of an unsolicited offer for control or 
       accumulation of stock by an individual shareholder or shareholders 
       acting as a group.

     - A detailed review of Mid-Peninsula.  This would cover the 
       following:

           - Historical financial performance evaluated against a relevant
             peer group of independent bank institutions;

           - Analysis of Mid-Peninsula's projections and their impact on 
             shareholder value;

           - Identification and analysis of the Company's shareholders; and

           - Review and analysis of the historical trading patterns of the 
             common stock.

     - Any additional financial analyses or advice as requested from time to 
       time by Mid-Peninsula.

     - Presentations to the Board of Directors of the Company on any of the 
       topics listed above as requested by management.

2.   For serving in the above capacity, Alex. Brown would receive a $25,000 
     retainer and be reimbursed for its out-of-pocket expenses applicable to
     the undertaking, including reasonable legal fees if appropriate.

3.   When requested by Mid-Peninsula, Alex. Brown would provide financial and 
     strategic analysis of and advice with respect to specific transactions 
     which, if consummated, would result in Mid-Peninsula acquiring, being 
     acquired by or otherwise combining with another entity. Specifically, with
     respect to any particular transaction, Alex. Brown would as requested:

     (a)  Render financial and strategic advice as it bears upon the 
          valuation of any potential transaction;

     (b)  Advise you as to the most appropriate form, consistent with law,
          accounting and business practice, for a proposed transaction;


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Mid-Peninsula Bancorp
May 28, 1996
Page 3


     (c)  Act as your agent and financial advisor in the negotiating process,
          working with you and your legal counsel and accountants. As your
          agent, Alex. Brown will engage in discussions on your behalf with
          other entities or their representatives only when authorized by 
          you to do so; and

     (d)  Render our opinion as to the fairness, from a financial point of 
          view, of the terms of a transaction to Mid-Peninsula shareholders.

4.   Our fee for assisting you in connection with specific transactions would
     be agreed between us in the context of a particular transaction. Among
     the factors to be considered would be:

     (a)  The scope and nature of our involvement;

     (b)  The complexity of the transaction;

     (c)  Whether we are requested to render a fairness opinion; and

     (d)  Customary investment banking fees for transactions of comparable 
          size.

     In addition, we understand that we may be asked to provide our opinions 
     and advice on smaller transactions that Mid-Peninsula may from time to 
     time consider; such advice will be provided at no additional fee.

5.   INDEMNIFICATION AND CONTRIBUTION.  In consideration of our services as 
     the Company's financial advisor hereunder, the Company agrees to 
     indemnify and hold harmless Alex. Brown and each of its directors, 
     officers, agents, employees and controlling persons (within the meaning 
     of the Securities Act of 1933, as amended) to the extent and as provided 
     in Addendum A attached hereto and incorporated herein by reference. The 
     provisions of this paragraph and Addendum A incorporated herein by 
     reference shall be effective as of the date hereof, and shall continue 
     in full force and effect until the termination of this agreement and, 
     thereafter, shall survive the termination of Alex. Brown's engagement 
     under this agreement and shall be binding upon any successors or assigns 
     of the Company.

6.   This agreement shall have an initial term extending until December 
     31, 1997, unless terminated prior thereto by the Company. Thereafter, 
     this agreement shall renew automatically from year-to-year upon the same 
     terms and conditions set forth herein until terminated in writing by 
     either Alex. Brown or Mid-Peninsula.



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Mid-Peninsula Bancorp
May 28, 1996
Page 4


If the foregoing letter correctly sets forth the terms of Alex. Brown's 
engagement, please sign and return to us the enclosed duplicate hereof.


                                  Very Truly Yours,

                                  ALEX. BROWN & SONS INCORPORATED


                                  By:  /s/ Jean-Luc Servat
                                       ----------------------------------
                                       Jean-Luc Servat
                                       Managing Director



Accepted and Agreed:

MID-PENINSULA BANCORP

By:  /s/ David L. Kalkbrenner
     -----------------------------------
     David L. Kalkbrenner
     President & Chief Executive Officer



                                                    Page 63 of 69 Pages




                                  ADDENDUM A


     In connection with our engagement described in the foregoing letter 
dated May 28, 1996, (the "Letter") to which this Addendum A is attached, the 
Company (as defined in the Letter) agrees to indemnify and hold harmless 
Alex. Brown & Sons Incorporated ("Alex. Brown") and each of its directors, 
officers, agents, employees and controlling persons (within the meaning of 
the Securities Act of 1933, as amended) from and against any losses, claims, 
damages or liabilities (or actions or proceedings in respect thereof) 
(collectively "Liabilities") related to or arising out of this engagement, 
and will reimburse Alex. Brown and each other person indemnified hereunder 
for all reasonable legal and other expenses as incurred in connection with 
defending any such Liabilities, whether or not Alex. Brown or any of its 
directors, officers, agents, employees and controlling persons is a named 
party thereto; provided, however, that the Company will not be liable in any 
such case (except cases arising out of the use of information provided by the 
Company with knowledge of its falsity) for Liabilities that a court of 
competent jurisdiction shall have found in a final judgment to have arisen 
primarily from the gross negligence, willful misconduct or bad faith of Alex. 
Brown or the party claiming a right to indemnification.

     In case any proceeding shall be instituted involving any person in 
respect of whom indemnity may be sought, such person (the "indemnified 
party") shall promptly notify the Company and the Company, upon request of 
the indemnified party, shall retain counsel reasonably satisfactory to the 
indemnified party to represent the indemnified party and any others the 
Company may designate in such proceeding and shall pay, as they are incurred, 
the fees and expenses of such counsel related to such proceeding. In any such 
proceeding, any indemnified party shall have the right to retain its own 
counsel at its own expense, except that the Company shall pay as incurred the 
reasonable fees and expenses of counsel retained by the indemnified party in 
the event that (i) the Company and the indemnified party shall have mutually 
agreed to the retention of such counsel or, (ii) the named parties to any 
such proceeding (including any impleaded parties) include both the Company 
and the indemnified party and representation of both parties by the same 
counsel would be inappropriate, in the reasonable opinion of the indemnified 
party, due to actual or potential differing interests between them.

     The Company shall not be liable for any settlement of any action or 
proceeding effected without its written consent, but if settled with such 
consent or if there be a final judgment for the plaintiff, the Company agrees 
to indemnify the indemnified parties to the extent set forth in this Addendum 
A. In addition, the Company will not, without the prior written consent of 
Alex. Brown, which shall not be unreasonably withheld, settle or compromise 
or consent to the entry of any judgment in any pending or threatened claim, 
action, suit or proceeding in respect of which indemnification may be sought 
hereunder (whether or not Alex. Brown or any indemnified party is an actual 
or potential party to such claim, action, suit or proceeding) unless such 
settlement, compromise or consent includes an unconditional release of Alex. 
Brown and each other indemnified party hereunder from all liability arising 
out of such claim, action, suit or proceeding.

                                                   Page 64 of 69 Pages


     In the event that a party is not entitled to indemnification hereunder 
because a court of competent jurisdiction has found the relevant Liability 
has arisen primarily from the gross negligence, willful misconduct or bad 
faith of Alex. Brown or such party, then Alex. Brown or such party shall 
reimburse to the Company all sums previously advanced hereunder.

     In the event a claim for indemnification under this Addendum A is 
determined to be unenforceable by a final judgment of a court of competent 
jurisdiction, then the Company shall contribute to the aggregate losses, 
claims, damages or liabilities to which Alex. Brown or its officers, 
directors, agents, employees or controlling persons may be subject in such 
amount as is appropriate to reflect the relative benefits received by each of 
the Company and the parties seeking contribution on the one hand, and the 
relative faults of the Company and the party seeking contribution on the 
other, as well as any other relevant equitable considerations.

     This indemnification shall apply to the original engagement as set forth 
in the Letter and any modification of the original engagement and the 
indemnification provided herein shall survive termination of our engagement 
and shall be binding upon any successors or assigns of the Company.


Acknowledged and Agreed:

MID-PENINSULA BANCORP

By:     /s/ David L. Kalkbrenner
      -------------------------------



Date:   May 28, 1996
      --------------------------------

JLS:cd



                                                        Page 65 of 69 Pages




                                [LETTERHEAD]



May 28, 1996



                                 ADDENDUM B

This Addendum B reflects qualifications relating to Sections 3(d) and 4 of 
the engagement agreement between Alex. Brown & Sons Incorporated ("Alex. 
Brown") and Mid-Peninsula Bancorp ("Mid-Peninsula" or the "Company") dated 
May 28, 1996.

This Addendum B is to confirm our understanding of the basis upon which Alex. 
Brown is being engaged to provide investment banking advice and services to 
Mid-Peninsula in connection with the proposed merger of equals (the 
"Transaction") by and between the Company and Cupertino National Bancorp 
("Cupertino").

1.  Alex. Brown will be engaged, as your sole and exclusive financial 
    advisor, to perform the following functions:

    (a)  Analyze, with the Company's management and Board of Directors, 
         the terms of any definitive acquisition agreement (the "Agreement") 
         entered into by and between the Company and Cupertino.

    (b)  Render our opinion (the "Opinion") as to the fairness, from a 
         financial point of view to the Company's shareholders, of the 
         Conversion Ratio (as defined in the Agreement) on the date of the 
         execution of the Agreement, update such opinion as required at or near
         the time of distribution of proxy materials by the Company and 
         bring-down such opinion as required at or near the time of closing of
         the Transaction. The nature and scope of the investigation which we 
         would conduct in order to be able to render our opinion will be 
         such as we would consider appropriate, and such opinion will be
         subject to customary assumptions and qualifications. Our opinion will 
         be in written form. Such opinion shall be solely for the use of the 
         Board of Directors in considering the Agreement and for inclusion in 
         the Company's proxy materials relating to the proposed Transaction. We
         understand and expect that the Company will use such Opinion in 
         connection with the proxy statement to be mailed to the Company's 
         shareholders seeking approval for the Transaction. The Company may not 


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Mid-Peninsula Bancorp
May 22, 1996
Page 2


         otherwise publish or refer to such opinion (either in its 
         entirety or through excerpts or summaries) or disclose the existence 
         of our engagement hereunder or describe or characterize the advice 
         provided by us to the Company without the prior written approval of 
         Alex. Brown, which approval shall not be unreasonably withheld, or 
         except as aforesaid or as otherwise required by applicable law.

2.  In consideration of our services as your financial advisor as described
    in Section 1 of this Addendum B, the Company agrees to compensate Alex.
    Brown as follows:

    (a)  Upon delivery the Opinion, Alex. Brown will be paid a non-refundable
         fee of $200,000, against which will be credited the $25,000 retainer
         fee previously paid in accordance with Section 2 of the Engagement 
         Agreement. Payment of this $175,000 shall be made in two installments: 
         $75,000 upon the rendering of the Opinion to the Board of Directors of 
         the Company and $100,000 upon inclusion of the Opinion in the Proxy 
         Statement to shareholders of the Company.

    (b)  In addition to the fee described above, the Company agrees to 
         reimburse Alex. Brown for all reasonable out-of-pocket expenses, 
         including fees and reimbursements of legal counsel, incurred by Alex. 
         Brown in carrying out its duties under this Addendum B. Fees and 
         reimbursements of legal counsel shall not exceed $2,000 without prior 
         approval of the Company.

3.  In consideration of our services as the Company's financial advisor under 
    this Addendum B and under the Engagement Agreement, the Company agrees 
    to indemnify and hold harmless Alex. Brown and each of its directors, 
    officers, agents, employees and controlling persons (within the meaning 
    of the Securities Act of 1933, as amended) to the extent and as provided 
    in Addendum A attached to the Engagement Agreement and incorporated 
    herein by reference. In addition, neither Alex. Brown nor any 
    indemnified person shall have any liability to the Company related to or 
    arising from the engagement described in this Addendum B, except for 
    liability for losses, claims, damages or expenses incurred by the Company 
    which are determined by a court of competent jurisdiction in a final 
    judgment to have arisen primarily from Alex. Brown's gross negligence, 
    willful misconduct or bad faith. The provisions of this Section 3 and 
    Addendum A incorporated herein by reference shall survive the 
    termination of Alex. Brown's engagement under this Addendum B and shall 
    be binding upon any successors or assigns of the Company.


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Mid-Peninsula Bancorp
May 22, 1996
Page 3


4.  In the event of consummation of the Transaction, Alex. Brown shall 
    have the right to disclose its participation in such Transaction, 
    including, without limitation, the placement of "tombstone" 
    advertisements in financial and other newspapers and journals, provided 
    that Alex. Brown will submit a copy of any such advertisements to the 
    Company for its approval, which approval shall not be unreasonably 
    withheld or delayed.

If the foregoing letter is in accordance with your understanding of the terms 
of our engagement, please sign and return to us the enclosed duplicate hereof.


                                  Very truly yours,

                                  ALEX. BROWN & SONS INCORPORATED


                                  By:  /s/ Jean-Luc Servat
                                       ----------------------------------
                                       Jean-Luc Servat
                                       Managing Director



Accepted and Agreed:

MID-PENINSULA BANCORP

By:  /s/ David L. Kalkbrenner
     -----------------------------------
     David L. Kalkbrenner
     President & Chief Executive Officer


Date:   May 28, 1996
      ----------------------------------



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