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

                           FORM 10-Q

[X]   Quarterly  report pursuant to Section 13 or  15(d)  of  the
Securities Exchange Act of 1934
For the quarterly period ended June 30, 1998 or

[  ]   Transition report pursuant to Section 13 or 15(d)  of  the
Securities Exchange Act of 1934
For the transition period from ________________to_____________

Commission File Number 0-13299


                DEAN WITTER CORNERSTONE FUND III
    (Exact name of registrant as specified in its charter)


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


c/o Demeter Management Corporation
Two  World  Trade  Center, 62 Fl.,  New  York,  NY          10048
(Address of principal executive offices)           (Zip Code)


Registrant's telephone number, including area code (212) 392-5454

(Former  name, former address, and former fiscal year, if changed
since last report)


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










<PAGE>
<TABLE>
                DEAN WITTER CORNERSTONE FUND III

             INDEX TO QUARTERLY REPORT ON FORM 10-Q

                         June 30, 1998
<CAPTION>

PART I. FINANCIAL INFORMATION
<S>                                                         <C>
Item 1. Financial Statements

   Statements of Financial Condition
   June 30, 1998 (Unaudited) and December 31, 1997............2

   Statements of Operations for the Quarters Ended
   June 30, 1998 and 1997 (Unaudited).........................3

   Statements of Operations for the Six Months Ended
   June 30, 1998 and 1997 (Unaudited).........................4

   Statements of Changes in Partners' Capital for the
   Six Months Ended June 30, 1998 and 1997 (Unaudited)........5

   Statements of Cash Flows for the Six Months Ended
   June 30, 1998 and 1997 (Unaudited).........................6

   Notes to Financial Statements (Unaudited)...............7-12

Item 2.  Management's Discussion and Analysis of Financial

Condition and Results of Operations..............13-18

PART II. OTHER INFORMATION

Item 1.  Legal Proceedings...................................19

Item 2.  Changes in Securities and Use of Proceeds...........19

Item 6.  Exhibits and Reports on Form 8-K................... 20



</TABLE>













<PAGE>
<TABLE>
                 PART I.  FINANCIAL INFORMATION

ITEM 1.  Financial Statements

                DEAN WITTER CORNERSTONE FUND III
               STATEMENTS OF FINANCIAL CONDITION

<CAPTION>

                                      June 30,     December 31,
                                        1998           1997
                                         $              $
                                    (Unaudited)
ASSETS
<S>                               <C>             <C>
Equity in commodity futures trading accounts:
 Cash                            40,755,926      39,762,715
 Net unrealized gain on open contracts1,485,060   1,938,295
 Net option premiums               (434,870)        (158,765)

 Total Trading Equity            41,806,116      41,542,245

 Due from DWR                       166,428          94,981
 Interest receivable (DWR)          144,065         145,100

 Total Assets                    42,116,609      41,782,326

LIABILITIES AND PARTNERS' CAPITAL

Liabilities

 Redemptions payable                422,473         429,759
 Accrued management fees            139,503         138,480
 Common administrative expenses payable     126,176        99,713

 Total Liabilities                   688,152        667,952

Partners' Capital

 Limited Partners (12,757.648 and
    13,352.334 Units, respectively)40,223,720    39,970,539
 General Partner (382.103 Units)   1,204,737      1,143,835

 Total Partners' Capital          41,428,457     41,114,374

 Total Liabilities and Partners' Capital 42,116,609    41,782,326


NET ASSET VALUE PER UNIT            3,152.91        2,993.52

<FN>

          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>
<TABLE>
                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF OPERATIONS
                           (Unaudited)

<CAPTION>

                                   For the Quarters Ended June 30,

                                     1998                1997
                                       $             $
REVENUES
<S>                           <C>            <C>
 Trading profit (loss):
    Realized                       510,583    2,474,925
    Net change in unrealized       (146,226)  (1,265,930)

      Total Trading Results        364,357    1,208,995

    Interest Income (DWR)          427,720       446,377

      Total Revenues               792,077    1,655,372


EXPENSES

    Brokerage commissions (DWR)    536,265      559,203
    Management fees                417,353      472,014
    Transaction fees and costs      54,388       54,481
          Common      administrative      expenses         18,632
17,030

      Total Expenses             1,026,638    1,102,728

NET INCOME (LOSS)                  (234,561)        552,644


NET INCOME (LOSS) ALLOCATION

    Limited Partners               (228,145)    538,088
    General Partner                  (6,416)     14,556


NET INCOME (LOSS) PER UNIT

    Limited Partners                 (16.79)      38.09
    General Partner                  (16.79)      38.09


<FN>



          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>

<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF OPERATIONS
                           (Unaudited)


<CAPTION>



                                For the Six Months Ended June 30,

                                     1998                1997
                                       $             $
REVENUES
<S>                         <C>              <C>
 Trading profit (loss):
    Realized                     3,823,062    6,703,472
    Net change in unrealized       (453,235)  (1,271,432)

      Total Trading Results      3,369,827    5,432,040

    Interest Income (DWR)          857,814        899,908

      Total Revenues             4,227,641    6,331,948


EXPENSES

    Brokerage commissions (DWR)  1,092,856    1,184,270
    Management fees                836,091      877,608
    Transaction fees and costs     110,653      114,093
         Common      administrative     expenses           32,174
36,352

      Total Expenses             2,071,774    2,212,323

NET INCOME                       2,155,867    4,119,625


NET INCOME ALLOCATION

    Limited Partners             2,094,965    4,016,671
    General Partner                 60,902      102,954


NET INCOME PER UNIT

    Limited Partners                159.39       269.44
    General Partner                 159.39       269.44

<FN>

          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>
<TABLE>


                DEAN WITTER CORNERSTONE FUND III
           STATEMENTS OF CHANGES IN PARTNERS' CAPITAL
        For the Six Months Ended June 30, 1998 and 1997
                          (Unaudited)


<CAPTION>


                          Units of
                        Partnership Limited   General
                          Interest   Partners Partner    Total



<S>                      <C>                                  <C>
<C>                              <C>
Partners' Capital,
    December   31,   1996      15,479.706             $40,997,752
$1,037,606                       $42,035,358

Offering     of    Units             1.841                  5,000
-                                   5,000

Net      Income                     -                   4,016,671
102,954                           4,119,625

Redemptions                  (993.087)                (2,912,582)
-                                  (2,912,582)

Partners' Capital,
    June   30,   1997          14,488.460             $42,106,841
$1,140,560                       $43,247,401




Partners' Capital,
    December   31,   1997      13,734.437             $39,970,539
$1,143,835                       $41,114,374

Offering   of  Units           5.184              15,998        -
15,998

Net      Income                     -                   2,094,965
60,902                            2,155,867

Redemptions                  (599.870)                (1,857,782)
-                                  (1,857,782)

Partners' Capital,
    June   30,   1998          13,139.751             $40,223,720
$1,204,737                       $41,428,457




<FN>

           The accompanying notes are an integral part
                 of these financial statements.

</TABLE>

<PAGE>
<TABLE>

                DEAN WITTER CORNERSTONE FUND III
                    STATEMENTS OF CASH FLOWS
                           (Unaudited)



<CAPTION>


                                 For the Six Months Ended June 30,

                                     1998              1997
                                        $            $
CASH FLOWS FROM OPERATING ACTIVITIES
<S>                         <C>                          <C>
   Net   income                        2,155,867                4
,119,625
 Noncash item included in net income:
      Net  change  in  unrealized         453,235               1
,271,432

 (Increase) decrease in operating assets:
      Net  option  premiums              276,105                (
251,237)
    Due from DWR                    (71,447)             (59,977)
    Interest receivable (DWR)         1,035              (5,728)

 Increase (decrease) in operating liabilities:
    Accrued management fees           1,023              2,996
    Common administrative expenses payable26,463         (10,677)
    Accrued brokerage commissions (DWR)-                 (2,747)
       Accrued    transaction   fees   and    costs             -
(4,251)

  Net  cash  provided  by  operating activities   2,842,281     5
,059,436


CASH FLOWS FROM FINANCING ACTIVITIES

 Offering of units                   15,998              5,000
   Decrease  in  redemptions  payable       (7,286)             (
313,285)
   Redemptions  of  units              (1,857,782)              (
2,912,582)

  Net  cash  used  for  financing activities     (1,849,070)    (
3,220,867)


   Net  increase  in  cash                993,211               1
,838,569

  Balance  at  beginning  of  period    39,762,715              4
0,587,011

  Balance  at  end  of  period         40,755,926               4
2,425,580


<FN>

          The accompanying notes are an integral part
                 of these financial statements.
</TABLE>
<PAGE>

                DEAN WITTER CORNERSTONE FUND III

                  NOTES TO FINANCIAL STATEMENTS

                           (Unaudited)

                                

The  financial statements include, in the opinion of  management,

all  adjustments necessary for a fair presentation of the results

of  operations and financial condition of Dean Witter Cornerstone

Fund  III  (the  "Partnership").  The  financial  statements  and

condensed  notes  herein should be read in conjunction  with  the

Partnership's December 31, 1997 Annual Report on Form 10-K.



1. Organization

Dean  Witter  Cornerstone  Fund  III  is  a  limited  partnership

organized  to  engage  in  the  speculative  trading  of  futures

contracts,    options    contracts,   and    forward    contracts

(collectively, "futures interests").  The Partnership is  one  of

the  Dean  Witter  Cornerstone Funds, comprised  of  Dean  Witter

Cornerstone Fund II, Dean Witter Cornerstone Fund III,  and  Dean

Witter  Cornerstone  Fund  IV.  The general  partner  is  Demeter

Management  Corporation ("Demeter").  The non-clearing  commodity

broker is Dean Witter Reynolds Inc. ("DWR"), with an unaffiliated

broker,  Carr  Futures  Inc.  ("Carr"),  providing  clearing  and

execution   services.  Both  Demeter  and  DWR  are  wholly-owned

subsidiaries  of Morgan Stanley Dean Witter & Co. ("MSDW").   The

trading   advisors  who  make  all  trading  decisions  for   the

Partnership   are   Abraham  Trading   Co.,   Welton   Investment

Corporation  (formerly,  Welton Investment  Systems  Corporation,

Inc.) and Sunrise Capital Management, Inc.



<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)



2. Related Party Transactions

The  Partnership's  cash  is on deposit  with  DWR  and  Carr  in

commodity trading accounts to meet margin requirements as needed.

DWR  pays  interest on these funds based on current 13-week  U.S.

Treasury  bill  rates.   Brokerage  expenses  incurred   by   the

Partnership are paid to DWR.


3. Financial Instruments

The Partnership trades futures, options, and forward contracts in

interest   rates,  stock  indices,  commodities  and  currencies.

Futures and forwards represent contracts for delayed delivery  of

an  instrument at a specified date and price.  Risk  arises  from

changes  in  the  value  of  these contracts  and  the  potential

inability  of  counterparties to perform under the terms  of  the

contracts.   There  are numerous factors which may  significantly

influence the market value of these contracts, including interest

rate  volatility.  At June 30, 1998 and December 31,  1997,  open

contracts were:

                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)


                               Contract or Notional Amount
                              June 30, 1998  December 31, 1997
                                    $                   $
Exchange-Traded Contracts
 Financial Futures:
   Commitments to Purchase       122,408,000     50,242,000
   Commitments to Sell            31,187,000     21,172,000
   Options Written                52,599,000          -
 Commodity Futures:
   Commitments to Purchase         7,475,000      8,055,000
   Commitments to Sell            26,339,000     31,622,000
   Options Written                   866,000          -
 Foreign Futures:
   Commitments to Purchase        98,266,000     50,870,000
   Commitments to Sell            46,681,000     42,064,000
   Options Written                     -              -
Off-Exchange-Traded
 Forward Currency Contracts
   Commitments to Purchase        24,223,000     27,863,000
   Commitments to Sell            34,530,000     41,794,000


A  portion of the amounts indicated as off-balance-sheet risk  in

forward   currency   contracts  is  due  to  offsetting   forward

commitments  to purchase and sell the same currency on  the  same

date   in   the   future.   These  commitments  are  economically

offsetting,  but are not offset in the forward market  until  the

settlement date.

                                
The  net  unrealized  gain on open contracts  is  reported  as  a

component  of  "Equity in Commodity futures trading accounts"  on

the  Statements of Financial Condition and totaled $1,485,060 and

$1,938,295 at June 30, 1998 and December 31, 1997, respectively.



Of  the $1,485,060 net unrealized gain on open contracts at  June

30, 1998, $1,264,297 related to exchange-traded futures contracts



<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)




and  $220,763  related  to off-exchange-traded  forward  currency

contracts.



Of  the  $1,938,295  net unrealized gain  on  open  contracts  at

December 31, 1997, $2,168,497 related to exchange-traded  futures

contracts  and $(230,202) related to off-exchange-traded  forward

currency contracts.



Exchange-traded futures contracts held by the Partnership at June

30,  1998 and December 31, 1997 mature through June 1999 and June

1998,   respectively.    Off-exchange-traded   forward   currency

contracts  held by the Partnership at June 30, 1998 and  December

31,   1997   mature  through  September  1998  and  March   1998,

respectively.



The   contract   amounts  in  the  above  table   represent   the

Partnership's  extent  of involvement in a  particular  class  of

financial  instrument, but not the credit  risk  associated  with

counterparty  non-performance.  The credit risk  associated  with

these  instruments  is limited to the amounts  reflected  in  the

Partnership's Statements of Financial Condition.



The Partnership also has credit risk because DWR and Carr act  as

the futures commission merchants or the counterparties, with

                                

<PAGE>

                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONTINUED)


respect  to  most  of the Partnership's assets.   Exchange-traded

futures and futures styled options contracts are marked to market

on  a  daily basis, with variations in value settled on  a  daily

basis.   Each  of DWR and Carr, as a futures commission  merchant

for  the Partnership's exchange-traded-futures and futures styled

options  contracts, is required, pursuant to regulations  of  the

Commodity Futures Trading Commission ("CFTC"), to segregate  from

their  own  assets, and for the sole benefit of  their  commodity

customers, all funds held by them with respect to exchange-traded

futures and futures styled option contracts, including an  amount

equal  to the net unrealized gain on all open futures and futures

styled  options contracts, which funds, in the aggregate, totaled

$42,020,223  and  $41,931,212 at June 30, 1998 and  December  31,

1997,  respectively.  With  respect  to  the  Partnership's  off-

exchange-traded forward currency contracts, there  are  no  daily

settlements  of variations in value nor is there any  requirement

that  an  amount equal to the net unrealized gain on open forward

contracts  be  segregated.  With respect  to  those  off-exchange

traded forward currency contracts, the Partnership is at risk  to

the  ability of Carr, the counterparty on all such contracts,  to

perform.  Carr's parent, Credit Agricole Indosuez, has guaranteed

to  the Partnership, payment of the net liquidating value of  the

transactions  in  the Partnership's account with Carr  (including

foreign currency contracts).




<PAGE>
                DEAN WITTER CORNERSTONE FUND III
            NOTES TO FINANCIAL STATEMENTS (CONCLUDED)


For  the  six  months  ended June 30, 1998  and  the  year  ended

December   31,   1997,  the  average  fair  value  of   financial

instruments held for trading purposes was as follows:




                                           June 30, 1998
                                       Assets        Liabilities
                                         $               $

Exchange-Traded Contracts:
  Financial Futures                 69,901,000       18,786,000
  Options on Financial Futures           -           30,619,000
  Commodity Futures                  6,533,000       25,401,000
  Options on Commodity Futures           -              326,000
  Foreign Futures                   75,410,000       27,048,000
Off-Exchange-Traded Forward
 Currency Contracts                 38,831,000       47,042,000


                                        December 31, 1997
                                       Assets        Liabilities
                                         $               $

Exchange-Traded Contracts:
  Financial Futures                 82,881,000       46,462,000
  Options on Financial Futures         698,000       64,639,000
  Commodity Futures                 26,095,000       21,377,000
  Options on Commodity Futures       1,117,000        4,712,000
  Foreign Futures                   44,764,000       26,219,000
  Options on Foreign Futures         7,229,000            -
Off-Exchange-Traded Forward
 Currency Contracts                 12,599,000       13,558,000

                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
                                
<PAGE>

Item   2.  MANAGEMENT'S  DISCUSSION  AND  ANALYSIS  OF  FINANCIAL
CONDITION AND RESULTS OF OPERATIONS


Liquidity - The Partnership's assets are deposited with  DWR,  as

non-clearing broker and with Carr, as clearing broker in separate

futures   interest  trading  accounts,  and  are  used   by   the

Partnership  as  margin  to engage in futures  interest  trading.

Such assets are held in either non-interest bearing bank accounts

or  in securities approved by the CFTC for investment of customer

funds.  The Partnership's assets held by DWR and Carr may be used

as  margin  solely  for  the Partnership's  trading.   Since  the

Partnership's  sole purpose is to trade in futures interests,  it

is expected that the Partnership will continue to own such liquid

assets for margin purposes.



The   Partnership's  investment  in  futures  interests  may   be

illiquid.  If  the price of a futures contract for  a  particular

commodity  has increased or decreased by an amount equal  to  the

"daily  limit," positions in the commodity can neither  be  taken

nor liquidated unless traders are willing to effect trades at  or

within  the  limit.   Commodity futures prices have  occasionally

moved the daily limit for several consecutive days with little or

no trading.  Such market conditions could prevent the Partnership

from  promptly  liquidating its commodity futures  positions  and

result in restrictions on redemptions.

                                

There  is  no limitation on daily price moves in trading  forward

contracts on foreign currencies.  The markets for some world

                                

<PAGE>

currencies  have low trading volume and are illiquid,  which  may

prevent  the  Partnership from trading in potentially  profitable

markets  or  prevent  the Partnership from  promptly  liquidating

unfavorable  positions  in  such markets  and  subjecting  it  to

substantial  losses.   Either of these  market  conditions  could

result in restrictions on redemptions.


Capital  Resources  The Partnership does not have,  nor  does  it

expect to have, any capital assets.  Redemptions and exchanges of

Units  of Limited Partnership Interest in the future will  affect

the amount of funds available for investment in futures interests

in  subsequent periods.  Since they are at the discretion of  the

Limited  Partners, it is not possible to estimate the amount  and

therefore, the impact of future redemptions and exchanges.



Results of Operations

For the Quarter and Six Months Ended June 30, 1998

For  the  quarter  ended June 30, 1998, the Partnership  recorded

total trading revenues including interest income of $792,077  and

posted  a  loss in Net Asset Value per Unit after expenses.   The

most significant net trading losses were incurred in the currency

markets  from  short German mark positions as its value  reversed

higher  during  April  after  showing  signs  of  trending  lower

previously.   Additional  currency losses  were  recorded  during

April  from  long British pound positions as its  value  weakened

relative  to  other  currencies.  In other markets,  losses  were

recorded in financial futures during April and June primarily

                                

<PAGE>

from  long  Australian bond futures positions as prices  reversed

lower  after  trending higher previously.  These losses,  coupled

with  smaller  losses incurred in British interest  rate  futures

trading, were partially offset by profits from long global  stock

index  futures  positions  as prices moved  higher  throughout  a

majority  of  the quarter.  In agricultural futures, losses  were

experienced  from  short corn and soybean  futures  positions  as

prices moved higher during the latter half of June. A portion  of

the  Partnership's  overall losses for the month  was  offset  by

gains  in soft commodities from short sugar futures positions  as

sugar  prices  moved  lower  during  April.   Additional  profits

recorded  during June from short positions in coffee futures,  as

well  as  during May and June from short positions in  crude  oil

futures,  helped  to  offset a portion  of  the  losses  for  the

quarter. Total expenses for the three months ended June 30,  1998

were  $1,026,638, resulting in a net loss of $234,561.  The value

of an individual Unit in the Partnership decreased from $3,169.70

at March 31, 1998 to $3,152.91 at June 30, 1998.



For  the  six months ended June 30, 1998, the Partnership  recorded

total trading revenues including interest income of $4,227,641  and

posted  a  gain in Net Asset Value per Unit.  The most  significant

profits  were  recorded  from long U.S. and  European  stock  index

futures  positions as prices in these markets trended  consistently

higher  throughout  the first six months of the  year.   Additional

profits were recorded from long European bond futures positions  as

prices  in  these markets trended higher during the first  quarter.

In

                                

<PAGE>

energies,  gains  were  recorded  from  short  crude  oil   futures

positions  as  oil prices declined during January and February,  as

tensions eased in the Middle East, and again during May and June on

reports  of increasing supplies.  Smaller gains were recorded  from

short  positions  in  sugar futures as sugar prices  trended  lower

between January and April.  A portion of these gains was offset  by

losses  recorded  in  the metals markets from long  silver  futures

positions  as  silver  prices reversed  lower  during  March  after

trending steadily higher during January and February and from short

gold  futures  positions  as  gold prices  reversed  higher  during

January.    Smaller  losses  were  recorded  in   currencies   from

transactions involving the British pound, as its value moved  in  a

trendless  pattern throughout a majority of the first half  of  the

year,  and  from  short German mark positions as  its  value  moved

higher versus the U.S. dollar during April.  Total expenses for the

six  months  ended June 30, 1998 were $2,071,774 resulting  in  net

income  of  $2,155,867.   The value of an individual  Unit  in  the

Partnership  increased  from $2,993.52  at  December  31,  1997  to

$3,152.91 at June 30, 1998.



For the Quarter and Six Months Ended June 30, 1997

For  the  quarter  ended June 30, 1997, the Partnership  recorded

total  trading  revenues including interest income of  $1,655,372

and  posted  an increase in Net Asset Value per Unit.   The  most

significant  trading gains were recorded in the soft  commodities

markets  from  long  coffee futures positions as  prices  trended

higher  during April and May.  Additional gains were recorded  in

the  currency markets from transactions involving the German mark

relative to the Japanese yen during June.  A portion of these

<PAGE>

gains was offset by losses recorded from choppy price movement in

the agricultural markets, particularly livestock and corn futures

during  the  quarter.  Losses were also experienced from  trading

crude  oil  futures as oil prices moved in a short-term  volatile

pattern.   In  financial futures trading, losses were experienced

from  trendless  price movement in global interest  rate  futures

throughout  a  majority  of  the quarter.   Smaller  losses  were

recorded  in the metals markets from long positions in most  base

metals  futures,  as prices moved lower during  April  and  June.

Total  expenses  for the three months ended June  30,  1997  were

$1,102,728 resulting in net income of $552,644.  The value of  an

individual  Unit in the Partnership increased from  $2,946.86  at

March 31, 1997 to $2,984.95 at June 30, 1997.

                                

For  the six months ended June 30, 1997, the Partnership recorded

total  trading  revenues including interest income of  $6,331,948

and  posted  an increase in Net Asset Value per Unit.   The  most

significant  trading gains were recorded in the soft  commodities

markets  from  long  coffee futures positions  as  coffee  prices

trended higher during January and February and again during April

and May.  Gains were also recorded in the currency markets during

January and February as a result of a strong upward trend in  the

value  of the U.S. dollar versus the Japanese yen and most  major

European  currencies.  In the agricultural markets, profits  were

recorded  from trading soybean and corn futures during March  and

June.   Smaller  gains  were experienced in  the  metals  markets

during  January and February from long zinc futures positions  as

most  base  metals  prices  moved  higher.   A  portion  of   the

Partnership's

<PAGE>

overall gains was offset by losses recorded from trendless  price

movement  in  Japanese and European interest rate futures  during

April  and May.  Trading gains experienced from long global stock

index futures positions as global equity prices trended higher in

May  and  June  helped to mitigate these losses.  Smaller  losses

were recorded in energies as gas and oil prices moved in a short-

term  volatile pattern for a majority of the first  half  of  the

year.  Total expenses for the six months ended June 30, 1997 were

$2,212,323, resulting in net income of $4,119,625.  The value  of

an individual Unit in the Partnership increased from $2,715.51 at

December 31, 1996 to $2,984.95 at June 30, 1997.


































<PAGE>
                                

                  PART II.   OTHER INFORMATION



Item 1.   LEGAL PROCEEDINGS

Previously  reported.  See Form 10-Q for the quarter ended  March

31, 1998.



Item 2.  CHANGES IN SECURITIES AND USE OF PROCEEDS

Dean  Witter  Cornerstone  Fund I ("Cornerstone  I"),  Dean  Witter

Cornerstone   Fund  II  ("Cornerstone  II"),  and  the  Partnership

collectively  registered  250,000  Units  of  Limited   Partnership

Interest ("Units") pursuant to a Registration Statement on Form  S-

1,  which  became  effective  on May 31,  1984  (the  "Registration

Statement")  (SEC  File  Numbers 2-88587; 88587-01;  88587-02).  As

contemplated  in  the Registration Statement, an  additional  fund,

Dean   Witter   Cornerstone  Fund  IV,   ("Cornerstone   IV"   and,

collectively   with   Cornerstone  I,  Cornerstone   II   and   the

Partnership,  the "Cornerstone Funds") was registered  pursuant  to

Post-Effective Amendment No. 5 to the Registration Statement, which

became effective on February 6, 1987. The managing underwriter  for

the Cornerstone Funds is DWR.


The  offering for the Partnership originally commenced on  May  31,

1984  and  currently continues with 74,405.186 Units  sold  through

June  30, 1998.  Through June 30, 1998, the Cornerstone Funds  have

sold  an  aggregate of 235,407.756 Units leaving  14,592.244  Units

remaining available for sale as of July 1, 1998.



The  aggregate  price of Units sold through June  30,  1998  with

respect to the Partnership is $137,132,762.

<PAGE>







Item 6. - EXHIBITS AND REPORTS ON FORM 8-K

          Reports on Form 8-K - No such reports have
          been filed for the quarter ended June 30, 1998.














































<PAGE>



                           SIGNATURE



Pursuant  to the requirements 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)

August 12, 1998                By: /s/ Lewis A. Raibley, III
                                       Lewis A. Raibley, III
                                       Chief Financial Officer




The  General  Partner which signed the above is  the  only  party
authorized  to  act  for the Registrant.  The Registrant  has  no
principal   executive  officer,  principal   financial   officer,
controller, or principal accounting officer and has no  Board  of
Directors.