UNITED STATES
                  SECURITIES AND EXCHANGE COMMISSION
                       Washington, D.C. 20549

                            FORM 10-K-A

[X]  Annual report pursuant to Section 13 or 15 (d) of the Securities Exchange
Act of 1934 [Fee Required]
For the fiscal year ended December 31, 1996 or

[ ]    Transition report pursuant to Section 13 or 15 (d) of the Securities
Exchange Act of 1934 [No Fee Required]
For the transition period from ______________ to __________________
Commission File Number 0-13299

                              DEAN WITTER CORNERSTONE FUND III

 (Exact name of registrant as specified in its Limited Partnership Agreement)

          NEW YORK                                    13-3190919
(State or other jurisdiction of                    (I.R.S. Employer
 incorporation of organization)                  Identification No.)

c/o Demeter Management Corp.
Two World Trade Center, New York, N.Y. - 62nd Flr.          10048
(Address of principal executive offices)                 (Zip Code)
       
Registrant's telephone number, including area code          (212) 392-5454

Securities registered pursuant to Section 12(b) of the Act:

Title of each class                                    Name of each exchange
                                                       on which registered

              None                                               None

Securities registered pursuant to Section 12(g) of the Act:

                            Units of Limited Partnership Interest

                                      (Title of Class)
 

                                      (Title of Class)

  Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of 
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.        Yes    X        No        

  Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K (section 229.405 of this chapter) is not contained
herein,and will not be contained, to the best of registrant's knowledge, in
definitive proxy or information statements incorporated by reference in Part
III of this Form 10-K or any amendment of this Form 10K. [ X ]

State the aggregate market value of the Units of Limited Partnership Interest 
held by non-affiliates of the registrant.  The aggregate market value shall be
computed by reference to the price at which units were sold, or the average bid
and asked prices of such units, as of a specified date within 60 days prior to
the date of filing: $46,954,013.46 at January 31, 1997.

                             DOCUMENTS INCORPORATED BY REFERENCE
                                        (See Page 1)
                                        <PAGE>
                                         SIGNATURES

       Pursuant to the requirement of Sections 13 or 15(d) of the
Securities Exchange Act of 1934, the registrant has duly caused this
report to be signed on its behalf by the undersigned, thereunto duly
authorized.
                            
                                   DEAN WITTER CORNERSTONE FUND III
                                          (Registrant)

                                   BY:  Demeter Management Corporation,
                                          General Partner

March 21, 1997                     BY: /s/ Mark J. Hawley               
                                           Mark J. Hawley, Director and
                                            President

       Pursuant to the requirements of the Securities Exchange Act of
1934, this report has been signed below by the following persons on
behalf of the registrant and in the capacities and on the dates
indicated. 

Demeter Management Corporation.

BY: /s/  Mark J. Hawley                                        March 21, 1997
          Mark J. Hawley, Director and
            President       

    /s/  Richard M. DeMartini                                  March 21, 1997
          Richard M. DeMartini, Director
            and Chairman of the Board


    /s/  Lawrence Volpe                                        March 21, 1997
          Lawrence Volpe, Director        
            

    /s/  Laurence E. Mollner                                   March 21, 1997
          Laurence E. Mollner, Director   
            

    /s/  Joseph G. Siniscalchi                                 March 21, 1997
          Joseph G. Siniscalchi, Director 

     
    /s/  Edward C. Oelsner III                                 March 21, 1997
          Edward C. Oelsner III, Director 


    /s/  Robert E. Murray                                      March 21, 1997
          Robert E. Murray, Director  


    /s/  Patti L. Behnke                                       March 21, 1997
          Patti L. Behnke, Chief Financial
           Officer


<PAGE>
                                        EXHIBIT INDEX
       
ITEM                                              METHOD OF FILING           

- 3.   Limited Partnership Agreement of
       the Partnership, dated as of
       December 7, 1983, as amended as                       
       of May 11, 1984.                                      (1)

-10.   Management Agreement among the 
       Partnership, Demeter Management
       Corporation and Sunrise Commodities
       Inc. dated as of November 15, 1983.                   (2)

-10.   Management Agreement among the
       Partnership, Demeter Management 
       Corporation and Computerized
       Commodity Advisory Inc. dated as 
       of June 18, 1986.                                     (3)

-10.   Dean Witter Cornerstone Funds
       Exchange Agreement, dated as of
       May 31, 1984.                                         (4)

-10.   Customer Agreement Between the
       Partnership and Dean Witter
       Reynolds Inc., dated as of May 31, 1984.              (5)

-13.   December 31, 1996 Annual Report to Limited Partners.  (6)



(1)    Incorporated by reference to Exhibit 3.01 to Partnership's
       Annual Report on Form 10-K for the fiscal year ended
       September 30, 1984.

(2)    Incorporated by reference to Exhibit 10.03 to the
       Partnership's Annual Report on Form 10-K for the fiscal year
       ended September 30, 1984.

(3)    Incorporated by reference to Exhibit 10.04 to the
       Partnership's Annual Report on Form 10-K for the fiscal year
       ended September 30, 1986.

(4)    Incorporated by reference to Exhibit 10.06 to the
       Partnership's Annual Report on Form 10-K for the fiscal year
       ended September 30, 1984.

(5)    Incorporated by reference to Exhibit 10.07 to the
       Partnership's Annual Report on Form 10-K for the fiscal year
       ended September 30, 1984.

(6)    Filed herewith.