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, 1999 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, 1999

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

   Statements of Financial Condition
   June 30, 1999 (Unaudited) and December 31, 1998............2

   Statements of Operations for the Quarters Ended
   June 30, 1999 and 1998 (Unaudited).........................3

   Statements of Operations for the Six Months Ended
   June 30, 1999 and 1998 (Unaudited).........................4

   Statements of Changes in Partners' Capital for the
   Six Months Ended June 30, 1999 and 1998 (Unaudited)........5

   Statements of Cash Flows for the Six Months Ended
   June 30, 1999 and 1998 (Unaudited).........................6

   Notes to Financial Statements (Unaudited)...............7-11

Item 2. Management's Discussion and Analysis of Financial

Condition and Results of Operations.............. 12-20

Item 3. Quantitative and Qualitative Disclosures about
        Market Risk ......................................20-32

PART II. OTHER INFORMATION

Item 1.  Legal Proceedings.................................. 33

Item 2.  Changes in Securities and Use of Proceeds........33-34

Item 6.  Exhibits and Reports on Form 8-K................... 34

</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,
                                        1999           1998
                                         $              $
                                    (Unaudited)
ASSETS
<S>                                     <C>            <C>
Equity in futures interests trading accounts:
 Cash                           35,428,932       38,504,975
 Net unrealized gain on open contracts2,153,381    2,102,810
 Net option premiums              (179,222)          (50,047)

      Total Trading Equity      37,403,091       40,557,738

 Due from DWR                      188,144           81,647
 Interest receivable (DWR)         114,124          120,465

      Total Assets              37,705,359       40,759,850

LIABILITIES AND PARTNERS' CAPITAL

Liabilities

 Redemptions payable               478,864          220,184
 Accrued administrative expenses   142,106          104,780
 Accrued management fees           124,795          135,067

      Total Liabilities            745,765          460,031

Partners' Capital

 Limited Partners (11,524.846 and
    12,193.413 Units, respectively)36,509,428    39,835,572
 General Partner (142.103 Units)     450,166         464,247

 Total Partners' Capital        36,959,594       40,299,819

  Total  Liabilities and Partners' Capital   37,705,359       40,
759,850


NET ASSET VALUE PER UNIT          3,167.89          3,266.97

<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,

                                     1999                1998
                                       $             $
REVENUES
<S>                             <C>          <C>
 Trading profit (loss):
    Realized                      221,630       510,583
    Net change in unrealized    1,503,917       (146,226)

      Total Trading Results     1,725,547       364,357

          Interest       Income       (DWR)               336,329
427,720

      Total Revenues            2,061,876       792,077


EXPENSES

    Brokerage commissions (DWR)   526,252       536,265
    Management fees               375,763       417,353
    Transaction fees and costs     57,173        54,388
    Administrative expenses        18,914        18,632

      Total Expenses              978,102     1,026,638

NET INCOME (LOSS)                1,083,774      (234,561)


NET INCOME (LOSS) ALLOCATION

    Limited Partners             1,070,901      (228,145)
    General Partner                 12,873        (6,416)

NET INCOME (LOSS) PER UNIT

      Limited   Partners                  90.59           (16.79)
General Partner                     90.59         (16.79)

<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,

                                     1999                1998
                                       $             $
REVENUES
<S>                             <C>          <C>
 Trading profit (loss):
    Realized                        (43,305)  3,823,062
                      Net   change   in   unrealized       50,571
(453,235)

      Total Trading Results          7,266    3,369,827

    Interest Income (DWR)          679,798       857,814

      Total Revenues               687,064      4,227,641


EXPENSES

    Brokerage commissions (DWR)  1,021,107    1,092,856
    Management fees                758,974      836,091
    Transaction fees and costs     102,935      110,653
    Administrative expenses         37,326         32,174

      Total Expenses             1,920,342     2,071,774

NET INCOME (LOSS)                (1,233,278)   2,155,867


NET INCOME (LOSS) ALLOCATION

    Limited Partners             (1,219,197)  2,094,965
    General Partner                 (14,081)     60,902

NET INCOME (LOSS) PER UNIT

    Limited Partners                 (99.08)     159.39
    General Partner                  (99.08)     159.39

<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, 1999 and 1998
                          (Unaudited)

<CAPTION>



                          Units of
                        Partnership Limited   General
                          Interest   Partners Partner    Total



<S>                           <C>                             <C>
<C>                              <C>
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





Partners' Capital,
    December   31,   1998      12,335.516             $39,835,572
$464,247                         $40,299,819

Net     Loss                       -                  (1,219,197)
(14,081)                         (1,233,278)

Redemptions                  (668.567)                (2,106,947)
-                                  (2,106,947)

Partners' Capital,
    June   30,   1999           11,666.949            $36,509,428
$450,166                          $36,959,594


<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,

                                     1999              1998
                                        $            $
CASH FLOWS FROM OPERATING ACTIVITIES
<S>                          <C>                         <C>
   Net  income  (loss)                 (1,233,278)              2
,155,867
 Noncash item included in net income (loss):
    Net change in unrealized         (50,571)            453,235

 (Increase) decrease in operating assets:
    Net option premiums             129,175              276,105
    Due from DWR                    (106,497)            (71,447)
Interest receivable (DWR)             6,341              1,035

 Increase (decrease) in operating liabilities:
          Accrued      administrative      expenses        37,326
26,463
          Accrued      management      fees              (10,272)
1,023

  Net  cash  provided  by  (used for)  operating  activities   (1
,227,776)                                       2,842,281


CASH FLOWS FROM FINANCING ACTIVITIES

  Offering of units                   -                    15,998
Increase (decrease) in redemptions payable258,680         (7,286)
Redemptions   of  units                (2,106,947)              (
1,857,782)

   Net   cash   used   for   financing  activities    (1,848,267)
(1,849,070)

 Net increase (decrease) in cash  (3,076,043)            993,211
     Balance     at     beginning    of    period      38,504,975
39,762,715

     Balance     at     end    of    period            35,428,932
40,755,926


<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, 1998 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,

options  and  forward contracts on foreign currencies  and  other

commodity  interests  (collectively, "futures  interests").   The

Partnership  is  one  of  the  Dean  Witter  Cornerstone   Funds,

comprised  of  Dean Witter Cornerstone Fund II, the  Partnership,

and  Dean  Witter Cornerstone Fund IV. The Partnership's  general

partner is Demeter Management Corporation ("Demeter").  The  non-

clearing  commodity broker is Dean Witter Reynolds  Inc.  ("DWR")

and  an unaffiliated clearing commodity broker, Carr Futures Inc.

("Carr"), provides clearing and execution services.  Both Demeter

and  DWR  are  wholly-owned subsidiaries of Morgan  Stanley  Dean

Witter  &  Co. ("MSDW"). The trading managers to the  Partnership

are  Abraham  Trading  Co.,  Welton  Investment  Corporation  and

Sunrise  Capital  Management  Inc., (collectively,  the  "Trading

Managers").





<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 futures

interests trading accounts to meet margin requirements as needed.

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

Treasury  bill rates.  The Partnership pays brokerage commissions

to DWR.



3.  Financial Instruments

The Partnership trades futures, options and forward contracts  on

foreign  currencies  and other commodity interests.  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.



In  June  1998, the Financial Accounting Standards  Board  issued

Statement  of  Financial Accounting Standard  ("SFAS")  No.  133,

"Accounting  for  Derivative Instruments and Hedging  Activities"

effective  for fiscal years beginning after June 15,  1999.   The

Partnership  elected  to adopt the provisions  of  SFAS  No.  133

beginning  with  the  fiscal year that ended December  31,  1998.

SFAS  No. 133 supersedes SFAS No. 119 and No. 105, which required

the



<PAGE>

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




disclosure of average aggregate fair values and contract/notional

values, respectively, of derivative financial instruments for  an

entity  which carries its assets at fair value.  The  application

of  SFAS  No.  133  does  not have a significant  effect  on  the

Partnership's financial statements.



The  net  unrealized  gain on open contracts  is  reported  as  a

component  of  "Equity in futures interests trading accounts"  on

the  Statements of Financial Condition and totaled $2,153,381 and

$2,102,810 at June 30, 1999 and December 31, 1998, respectively.



Of  the $2,153,381 net unrealized gain on open contracts at  June

30,  1999,  $2,087,450  related to  exchange-traded  futures  and

futures-styled  option  contracts and  $65,931  related  to  off-

exchange-traded forward currency contracts.



Of  the  $2,102,810  net unrealized gain  on  open  contracts  at

December 31, 1998, $2,250,314 related to exchange-traded  futures

and futures-styled option contracts and $(147,504) related to off-

exchange-traded forward currency contracts.



Exchange-traded futures and futures-styled options contracts held

by  the Partnership at June 30, 1999 and December 31, 1998 mature

through June 2000 and June 1999, respectively. Off-exchange-



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




traded forward currency contracts held by the Partnership at June

30,  1999 and December 31, 1998 mature through September 1999 and

March 1999, respectively.



The  Partnership  is subject to the credit risk  associated  with

counterparty  non-performance.  The credit risk  associated  with

the  instruments in which the Partnership is involved is  limited

to  the  amounts  reflected  in the Partnership's  Statements  of

Financial  Condition.  DWR and Carr act as the futures commission

merchants  or  the counterparties with 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  all   of   the

Partnership's exchange-traded futures and futures-styled  options

contracts, are 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 options 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

$37,516,382  and  $40,755,289 at June 30, 1999 and  December  31,

1998, respectively.





<PAGE>

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




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

sole  counterparty on all of 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>
Item   2.  MANAGEMENT'S  DISCUSSION  AND  ANALYSIS  OF  FINANCIAL
CONDITION AND RESULTS OF OPERATIONS

Liquidity -  Assets of the Partnership are deposited with DWR  as

non-clearing  broker  and  Carr as clearing  broker  in  separate

futures interest trading accounts. 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, from time

to time, be illiquid.  Most United States futures exchanges limit

fluctuations in certain futures interest prices during  a  single

day  by  regulations  referred to as  "daily  price  fluctuations

limits" or "daily limits".  Pursuant to such regulations,  during

a  single trading day no trades may be executed at prices  beyond

the  daily limit.  If the price for a particular futures interest

has increased or decreased by an amount equal to the daily limit,

positions  in  such  futures interest can neither  be  taken  nor

liquidated  unless  traders are willing to effect  trades  at  or

within  the  limit.   Futures interests 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 futures interests and  result  in

restrictions on redemptions.





<PAGE>

There  is  no limitation on daily price moves in trading  forward

contracts  on  foreign  currency.  The  markets  for  some  world

currencies  have low trading volume and are illiquid,  which  may

prevent  the  Partnership from trading in potentially  profitable

markets  or  from  promptly  liquidating  unfavorable  positions,

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.  Future  redemptions  and

exchanges  of  Units of Limited Partnership Interest  ("Unit(s)")

will  affect  the  amount of funds available  for  investment  in

futures interests in subsequent periods.  Since they are  at  the

discretion  of 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, 1999

For the quarter ended June 30, 1999, the Partnership recorded

total  trading  revenues including interest income of  $2,061,876

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

significant  gains  were recorded in global stock  index  futures

from  long positions in S&P 500 Index futures as domestic  equity

prices moved higher during April, following an interest rate  cut

by  the  European Central Bank, and during late  June  after  the

Federal  Reserve said it was shifting to a neutral bias following

an increase in the Federal Funds rate on June 30.  Additional

<PAGE>

gains  were recorded during May and June from short positions  in

U.S.  interest rate futures as domestic bond prices  declined  in

anticipation of an interest rate increase by the Federal  Reserve

late  in the quarter.  In the agricultural markets, profits  were

recorded from short futures positions in soybeans and soybean oil

as  prices  in  these markets fell during May  and  June  due  to

favorable  planting  forecasts  and  bearish  supply-demand   and

production  data.   These gains were partially offset  by  losses

incurred  from long positions in most base metals as prices  fell

significantly during late May amid large supply, low  demand  and

as  the  possibility of production cuts in the near future seemed

unlikely.   Smaller  losses were recorded in the  energy  markets

during  June from long positions in natural gas futures as prices

moved  lower  due to higher-than-expected storage levels.   Total

expenses  for the three months ended June 30, 1999 were $978,102,

resulting  in  net income of $1,083,774.  The  value  of  a  Unit

increased from $3,077.30 at March 31, 1999 to $3,167.89  at  June

30, 1999.



For  the six months ended June 30, 1999, the Partnership recorded

total trading revenues including interest income of $687,064 and,

after  expenses, posted a decrease in Net Asset Value  per  Unit.

The  most significant net trading losses were recorded from short

positions in Japanese government bond futures as prices increased

during January and February.  During January, Japanese government

bond  prices moved higher in a "flight-to-quality" due to renewed

concerns regarding the Brazilian economy.  Prices in this  market

continued to increase during February amid growing speculation

<PAGE>

that  a  rise  in Japanese bond yields would result  in  Japanese

investors  replacing  international  bonds  with  yen-denominated

debt.  In  metals,  losses were incurred  during  May  from  long

positions  in  most base metals as prices declined amid  abundant

supplies,  weak demand and as the possibility of production  cuts

in  the  near future seemed unlikely.  Smaller losses experienced

from  long  British pound positions, as the value  of  the  pound

weakened  versus the U.S. dollar during May due  to  fear  of  an

interest rate cut by the Bank of England, more than offset  gains

from  short positions in the Swiss franc and the European  common

currency,  the euro, as their values weakened versus  the  dollar

throughout the first half of the year.  A portion of the  overall

Partnership losses for the first six months of 1999 was offset by

gains  recorded  in the agricultural markets from  short  futures

positions  in soybeans and soybean oil as prices declined  during

January  and February, and again during May and June,  due  to  a

healthy  South  American crop, fears that  Brazil  will  increase

exports  to support its economy and a continued decline in  world

demand.    Additional  gains  were  recorded  from  long  futures

positions  in  crude oil as oil prices climbed during  the  first

quarter on news that both OPEC and non-OPEC countries had reached

an agreement to cut total output beginning April 1st.  Oil prices

received  an  added  boost during the second  quarter  as  prices

reached  a  19-month high due to declining inventory  levels  and

increasing demand.  Total expenses for the six months ended  June

30,  1999 were $1,920,342, resulting in a net loss of $1,233,278.

The value of a Unit decreased from $3,266.97 at December 31, 1998

to $3,167.89 at June 30, 1999.



<PAGE>

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,

after  expenses, posted a decrease in Net Asset Value  per  Unit.

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  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



<PAGE>

value  of  a Unit 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  an  increase  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 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



<PAGE>

of  $2,155,867.   The value of a Unit increased from  $2,993.52  at

December 31, 1997 to $3,152.91 at June 30, 1998.



Year  2000 Problem.  Commodity pools, like financial and business

organizations  and individuals around the world,  depend  on  the

smooth functioning of computer systems.  Many computer systems in

use  today cannot recognize the computer code for the year  2000,

but revert to 1900 or some other date.  This is commonly known as

the  "Year  2000  Problem". The Partnership  could  be  adversely

affected  if computer systems used by it or any third party  with

whom  it has a material relationship do not properly process  and

calculate date-related information and data concerning  dates  on

or  after January 1, 2000.  Such a failure could adversely affect

the  handling or determination of futures trades and  prices  and

other services.



MSDW  began its planning for the Year 2000 Problem in  1995,  and

currently  has several hundred employees working on  the  matter.

It  has developed its own Year 2000 compliance plan to deal  with

the  problem and had the plan approved by the company's executive

management,   Board  of  Directors  and  Information   Technology

Department. Demeter is coordinating with MSDW to address the Year

2000  Problem  with  respect to Demeter's computer  systems  that

affect  the  Partnership.  This includes  hardware  and  software

upgrades, systems consulting and computer maintenance.



Beyond  the  challenge  facing  internal  computer  systems,  the

systems failure of any of the third parties with whom the

<PAGE>

Partnership  has a material relationship - the futures  exchanges

and  clearing organizations through which it trades, Carr, or the

Trading  Managers - could result in a material financial risk  to

the  Partnership.  All  U.S. futures  exchanges  are  subject  to

monitoring  by the CFTC of their Year 2000 preparedness  and  the

major  foreign futures exchanges are also expected to be  subject

to market-wide testing of their Year 2000 compliance during 1999.

Demeter  intends to monitor the progress of Carr and the  Trading

Managers throughout 1999 in their Year 2000 compliance and, where

applicable,  to  test its external interface with  Carr  and  the

Trading Managers.



A  worst case scenario would be one in which trading of contracts

on  behalf  of the Partnership becomes impossible as a result  of

the  Year 2000 problem encountered by any third parties.  A  less

catastrophic  but  more likely scenario would  be  one  in  which

trading  opportunities diminish as a result of technical problems

resulting  in  illiquidity  and  fewer  opportunities   to   make

profitable trades. MSDW has begun developing various "contingency

plans" in the event that the systems of such third parties  fail.

Demeter  intends  to  consult closely with MSDW  in  implementing

those  plans.  Despite the best efforts of both Demeter and MSDW,

however,  it is possible that these steps will not be  sufficient

to avoid any adverse impact to the Partnership.


Risks  Associated  With  the Euro.  On January  1,  1999,  eleven

countries in the European Union established fixed conversion



<PAGE>

rates on their existing sovereign currencies and converted  to  a

common   single  currency  (the  "euro").   During  a  three-year

transition  period,  the sovereign currencies  will  continue  to

exist  but  only as a fixed denomination of the euro.  Conversion

to the euro prevents the Trading Managers from trading in certain

currencies and thereby limits their ability to take advantage  of

potential market opportunities that might otherwise have  existed

had  separate  currencies been available  to  trade.  This  could

adversely affect the performance results of the Partnership.



Item  3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES  ABOUT  MARKET
RISK

Introduction


The  Partnership  is a commodity pool engaged  primarily  in  the

speculative  trading of futures interests.  The market  sensitive

instruments  held  by  the Partnership are  acquired  solely  for

speculative   trading  purposes  and,  as  a   result,   all   or

substantially all of the Partnership's assets are subject to  the

risk  of trading loss.  Unlike an operating company, the risk  of

market sensitive instruments is integral, not incidental, to  the

Partnership's primary business activities.



The  futures interests traded by the Partnership involve  varying

degrees  of  related  market risk.  Such  market  risk  is  often

dependent  upon  changes in the level or volatility  of  interest

rates,   exchange  rates,  and/or  market  values  of   financial

instruments and commodities.  Fluctuations in related market risk



<PAGE>

based  upon the aforementioned factors result in frequent changes

in  the  fair  value  of the Partnership's open  positions,  and,

consequently, in its earnings and cash flow.



The  Partnership's  total market risk is  influenced  by  a  wide

variety  of factors, including the diversification effects  among

the Partnership's existing open positions, the volatility present

within  the  market(s), and the liquidity of the  market(s).   At

varying  times,  each of these factors may act to  exacerbate  or

mute the market risk associated with the Partnership.



The  Partnership's past performance is not necessarily indicative

of   its   future  results.   Any  attempt  at  quantifying   the

Partnership's  market  risk  must be qualified  by  the  inherent

uncertainty  of its speculative trading, which may  cause  future

losses and volatility (i.e. "risk of ruin") far in excess of  the

Partnership's   experience   to  date   and/or   any   reasonable

expectation premised upon historical changes in the fair value of

its market sensitive instruments.


Quantifying the Partnership's Trading Value at Risk


The    following    quantitative   disclosures   regarding    the

Partnership's  market  risk  exposures  contain  "forward-looking

statements"  within  the meaning of the safe  harbor  from  civil

liability  provided for such statements by the Private Securities

Litigation  Reform Act of 1995 (set forth in Section 27A  of  the

Securities Act of 1933 and Section 21E of the Securities Exchange

Act of 1934).  All

<PAGE>

quantitative disclosures in this section are deemed to be forward-

looking  statements for purposes of the safe harbor,  except  for

statements of historical fact.



The Partnership accounts for open positions on the basis of mark-

to-market accounting principles.  As such, any loss in  the  fair

value  of  the Partnership's open positions is directly reflected

in  the  Partnership's earnings, whether realized or  unrealized,

and  the  Partnership's cash flow, as profits and losses on  open

positions of exchange-traded futures interests are settled  daily

through variation margin.



The  Partnership's  risk exposure in the various  market  sectors

traded  by  the Trading Managers is estimated below in  terms  of

Value  at Risk ("VaR"). The VaR model employed by the Partnership

incorporates numerous variables that could impact the fair  value

of   the   Partnership's  trading  portfolio.   The   Partnership

estimates VaR using a model based on historical simulation with a

confidence   level   of  99%.   Historical  simulation   involves

constructing  a  distribution of hypothetical  daily  changes  in

trading  portfolio  value.  The VaR model  generally  takes  into

account linear exposures to price and interest rate risk.  Market

risks  that are incorporated in the VaR model include equity  and

commodity prices, interest rates, foreign exchange rates, as well

as   correlation   that  exists  among  these   variables.    The

hypothetical  changes  in  portfolio value  are  based  on  daily

observed percentage changes in key market indices or other market

factors  ("market  risk  factors")  to  which  the  portfolio  is

sensitive.  In the case of the

<PAGE>

Partnership's   VaR,   the  historical  observation   period   is

approximately  four  years.  The Partnership's  one-day  99%  VaR

corresponds to the negative change in portfolio value that, based

on  observed  market risk factor moves, would have been  exceeded

once in 100 trading days.



VaR models such as the Partnership's are continually evolving  as

trading  portfolios  become more diverse and modeling  techniques

and systems capabilities improve.  It must also be noted that the

VaR  model is used to quantify market risk for historic reporting

purposes  only  and  is  not utilized by either  Demeter  or  the

Trading Managers in their daily risk management activities.



The Partnership's Value at Risk in Different Market Sectors


The  following  table  indicates  the  VaR  associated  with  the

Partnership's open positions as a percentage of total Net  Assets

by market category as of June 30, 1999.  As of June 30, 1999, the

Partnership's total capitalization was approximately $37 million.

     Primary Market             June 30, 1999
     Risk Category              Value at Risk

     Equity                         (2.24)%

     Interest Rate                  (1.11)

     Currency                       (1.95)

     Commodity                      (1.01)

     Aggregate Value at Risk        (3.63)%







<PAGE>

Aggregate  value  at  risk represents the aggregate  VaR  of  the

Partnership's open positions and not the sum of the  VaR  of  the

individual categories listed above.  Aggregate VaR will be  lower

as  it  takes into account correlation among different  positions

and categories.


The  table  above  represents the VaR  of  the  Partnership's  open

positions   at   June  30,  1999  only  and  is   not   necessarily

representative  of  either  the  historic  or  future  risk  of  an

investment in the Partnership.  As the Partnership's sole  business

is  the  speculative  trading of primarily futures  interests,  the

composition  of  its  portfolio  of  open  positions   can   change

significantly  over any given time period or even within  a  single

trading  day.   Such  changes  in open positions  could  materially

impact  market  risk  as  measured  by  VaR  either  positively  or

negatively.



The  table below supplements the quarter-end VaR by presenting  the

Partnership's  high, low and average VaR as a percentage  of  total

Net  Assets for the four quarterly reporting periods from  July  1,

1998 through June 30, 1999.

Primary Market Risk Category        High      Low      Average

Equity                             (2.24)%   (0.08)%   (0.93)%

Interest Rate                      (1.74)    (0.43)    (1.15)
Currency                           (1.95)    (0.72)    (1.28)
Commodity                          (1.01)    (0.68)    (0.80)

Aggregate Value at Risk            (3.63)%   (1.61)%   (2.36)%





<PAGE>
Limitations on Value at Risk as an Assessment of Market Risk


The  face  value  of  the  market sector instruments  held  by  the

Partnership is typically many times the applicable margin  require-

ments,  as such margin requirements generally range between 2%  and

15%  of  contract  face value.  Additionally, due  to  the  use  of

leverage, the face value of the market sector instruments  held  by

the Partnership is typically many times the total capitalization of

the Partnership.  The financial magnitude of the Partnership's open

positions thus creates a      "risk of ruin" not typically found in

other  investment  vehicles.   Due to  the  relative  size  of  the

positions held, certain market conditions may cause the Partnership

to  incur losses greatly in excess of VaR within a short period  of

time.  The foregoing VaR tables, as well as the past performance of

the  Partnership, gives no indication of such "risk  of  ruin".  In

addition, VaR risk measures should be interpreted in light  of  the

methodology's  limitations,  which  include  the  following:   past

changes  in  market  risk factors will not  always  yield  accurate

predictions of the distributions and correlations of future  market

movements;  changes  in  portfolio  value  in  response  to  market

movements  may differ from the responses implicit in a  VaR  model;

published  VaR results reflect past trading positions while  future

risk  depends on future positions; VaR using a one-day time horizon

does not fully capture the market risk of positions that cannot  be

liquidated or hedged within one day; and the historical market risk

factor  data  used  for  VaR estimation may  provide  only  limited

insight  into  losses that could be incurred under certain  unusual

market movements.





<PAGE>

The  foregoing  VaR tables present the results of the Partnership's

VaR  for each of the Partnership's market risk exposures and on  an

aggregate  basis  at  June 30, 1999 and for the  end  of  the  four

quarterly  reporting  periods from July 1, 1998  through  June  30,

1999.  Since  VaR is based on historical data, VaR  should  not  be

viewed   as   predictive  of  the  Partnership's  future  financial

performance or its ability to manage and monitor risk and there can

be  no  assurance  that  the  Partnership's  actual  losses  on   a

particular  day will not exceed the VaR amounts indicated  or  that

such losses will not occur more than 1 in 100 trading days.



Non-Trading Risk

The  Partnership  has non-trading market risk on its  foreign  cash

balances not needed for margin.  However, such balances, as well as

any   market   risk  they  may  represent,  are  immaterial.    The

Partnership  also  maintains a substantial  portion  (approximately

85%)  of its available assets in cash at DWR.  A decline in  short-

term  interest  rates will result in a decline in the Partnership's

cash  management  income. This cash flow  risk  is  not  considered

material.



Materiality,  as  used  throughout this section,  is  based  on  an

assessment  of  reasonably  possible  market  movements   and   the

potential losses caused by such movements, taking into account  the

leverage,  optionality and multiplier features of the Partnership's

market sensitive instruments.



Qualitative Disclosures Regarding Primary Trading Risk Exposures

The following qualitative disclosures regarding the Partnership's

<PAGE>

market  risk exposures - except for (i) those disclosures that  are

statements of historical fact and (ii) the descriptions of how  the

Partnership manages its primary market risk exposures -  constitute

forward-looking statements within the meaning of Section 27A of the

Securities Act and Section 21E of the Securities Exchange Act.  The

Partnership's  primary  market  risk  exposures  as  well  as   the

strategies used and to be used by Demeter and the Trading  Managers

for  managing such exposures are subject to numerous uncertainties,

contingencies  and risks, any one of which could cause  the  actual

results  of  the  Partnership's risk controls to differ  materially

from  the objectives of such strategies.  Government interventions,

defaults  and  expropriations, illiquid markets, the  emergence  of

dominant  fundamental  factors,  political  upheavals,  changes  in

historical   price   relationships,  an  influx   of   new   market

participants,  increased regulation and many  other  factors  could

result  in  material losses as well as in material changes  to  the

risk   exposures  and  the  risk  management  strategies   of   the

Partnership.    Investors  must  be  prepared  to   lose   all   or

substantially all of their investment in the Partnership.



The  following  were  the primary trading  risk  exposures  of  the

Partnership  as  of  June 30, 1999, by market sector.   It  may  be

anticipated  however,  that  these  market  exposures   will   vary

materially over time.

      Equity.  The primary market exposure in the Partnership is in

the  stock index sector.  The primary equity exposure is to  equity

price risk in the G-7 countries.  The stock index futures traded by

<PAGE>

the  Partnership  are by law limited to futures  on  broadly  based

indices.   As of June 30, 1999, the Partnership's primary exposures

were  in the S&P 500 (U.S.), NASDAQ (U.S.) and Nikkei (Japan) stock

indices.   The  Partnership is primarily exposed  to  the  risk  of

adverse  price trends or static markets in the U.S.,  European  and

Japanese  indices.   (Static markets would not cause  major  market

changes  but would make it difficult for the Partnership  to  avoid

being "whipsawed" into numerous small losses).

      Interest  Rate.   The  second largest  market  exposure  this

quarter  is  in  the  interest rate complex.  Exposure  was  spread

across the U.S., German, Australian, Spanish, and Japanese interest

rate sectors.  Interest rate movements directly affect the price of

the  sovereign  bond futures positions held by the Partnership  and

indirectly  affect  the  value  of its  stock  index  and  currency

positions.   Interest  rate movements in one  country  as  well  as

relative  interest  rate  movements  between  countries  materially

impact  the Partnership's profitability.  The Partnership's primary

interest  rate exposure is generally to interest rate  fluctuations

in  the  United States and the other G-7 countries.   However,  the

Partnership also takes futures positions in the government debt  of

smaller  nations  - e.g. Australia and Spain.  Demeter  anticipates

that  G-7  and  Australian interest rates will remain  the  primary

interest  rate  exposure  of the Partnership  for  the  foreseeable

future.  The changes in interest rates, which have the most  effect

on  the Partnership, are changes in long-term, as opposed to short-

term rates.  Most of the speculative futures positions held by  the

Partnership are in



<PAGE>

medium-to-long term instruments.  Consequently, even  a  material

change  in  short-term  rates would have  little  effect  on  the

Partnership, were the medium-to-long term rates to remain steady.

     Currency. The Partnership's currency exposure is to exchange

rate  fluctuations,  primarily  fluctuations  which  disrupt  the

historical pricing relationships between different currencies and

currency  pairs.  Interest rate changes as well as political  and

general  economic  conditions influence these fluctuations.   The

Partnership  trades  in  a large number of currencies,  including

cross-rates - i.e., positions between two currencies  other  than

the   U.S.   dollar.   For  the  second  quarter  of  1999,   the

Partnership's  major exposures were in the Euro currency  crosses

and  outright U.S. dollar positions.  (Outright positions consist

of  the U.S. dollar vs. other currencies.  These other currencies

include  the  major  and  minor currencies).   Demeter  does  not

anticipate  that  the risk profile of the Partnership's  currency

sector  will  change significantly in the future.   The  currency

trading  Value  at  Risk figure includes foreign  margin  amounts

converted  into  U.S. dollars with an incremental  adjustment  to

reflect  the  exchange  rate risk inherent  to  the  dollar-based

Partnership in expressing Value at Risk in a functional  currency

other than dollars.

     Commodity.

     Soft  Commodities and Agriculturals.  On June 30, 1999,  the

Partnership  had a reasonable amount of exposure in  the  markets

that comprise these sectors.  Most of the exposure, however,  was

<PAGE>

in  the  corn,  coffee and soybean markets.   Supply  and  demand

inequalities,  severe weather disruption and market  expectations

affect price movements in these markets.

     Metals. The Partnership's primary metals market exposure  is

to  fluctuations  in  the  price of gold  and  silver.   Although

certain  Trading  Managers will, from time to  time,  trade  base

metals  such as aluminum, copper, nickel and lead, the  principal

market  exposures  of the Partnership have consistently  been  in

precious  metals,  gold and silver.  The Trading  Managers'  gold

trading has been increasingly limited due to the long-lasting and

mainly non-volatile decline in the price of gold over the last 10-

15  years.   However, silver prices have remained  volatile  over

this  period, and the Trading Managers have, from time  to  time,

taken   substantial  positions  as  they  have  perceived  market

opportunities  to  develop.  Demeter anticipates  that  gold  and

silver  will  remain the primary metals market exposure  for  the

Partnership.

     Energy.  On June 30, 1999, the Partnership's energy exposure

was  shared  by  futures contracts in the  oil  and  natural  gas

markets.   Price movements in these markets result from political

developments  in  the  Middle East, weather patterns,  and  other

economic  fundamentals.  As oil prices have  broken  out  of  low

price  ranges  achieved in 1998, it is possible  that  volatility

will  increase as well.  Significant profits and losses have been

and  are  expected to continue to be experienced in this  market.

Natural gas, also a primary energy market exposure, has exhibited

<PAGE>                              more volatility than the  oil

markets  on  an  intra-day and daily basis  and  is  expected  to

continue in this choppy pattern.



Qualitative Disclosures Regarding Non-Trading Risk Exposure

The  following  was  the only non-trading risk  exposure  of  the

Partnership as of June 30, 1999:



Foreign  Currency  Balances.  The Partnership's  primary  foreign

currency  balances  are in Swiss francs, euros,  British  pounds,

Japanese yen and Mexican pesos. The Partnership controls the non-

trading  risk  of  these balances by regularly  converting  these

balances  back  into dollars upon liquidation of  the  respective

position.



Qualitative Disclosures Regarding Means of Managing Risk Exposure

The  means  by  which the Partnership and the  Trading  Managers,

severally,  attempt to manage the risk of the Partnership's  open

positions  are  essentially the same  in  all  market  categories

traded.   Demeter  attempts  to manage the  Partnership's  market

exposure  by  (i)  diversifying the  Partnership's  assets  among

different  Trading  Managers, each of whose strategies  focus  on

different  market  sectors  and  trading  approaches,  and  (ii),

monitoring  the performance of the Trading Managers  on  a  daily

basis.     In    addition,   the   Trading   Managers   establish

diversification  guidelines, often set in terms  of  the  maximum

margin to be committed to positions in any one market sector or



<PAGE>

market  sensitive instrument.  One should be aware  that  certain

Trading  Managers  treat their risk control  policies  as  strict

rules, whereas others treat such policies as general guidelines.



Demeter monitors and controls the risk of the Partnership's  non-

trading   instrument,  cash,  which  is  the   only   Partnership

investment directed by Demeter, rather than the Trading Managers.











































<PAGE>
                   PART II.  OTHER INFORMATION



Item 1.   LEGAL PROCEEDINGS

The  following supplements Legal Proceedings previously disclosed

in the Partnership's 1998 Form 10-K:



With   respect   to  the  plaintiff's  consolidated   action   in

California, on July 1, 1999, the Superior Court of the  State  of

California, ruling from the bench, denied the plaintiffs'  motion

to have their lawsuit certified as a class action, stating, among

other  things,  that plaintiffs' lawsuit did not  present  common

questions of fact.



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 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 Cornerstone III originally commenced on  May  31,

1984  and  currently continues with 74,405.186 Units  sold  through

July

<PAGE>

1, 1999. The aggregate price of Units sold through July 1, 1999 was

$137,132,762.



For the Cornerstone Funds in aggregate, 235,430.680 Units have been

sold  through  July  1,  1999, leaving 14,569.320  Units  remaining

available for sale as of July 1, 1999.



Effective September 30, 1984, Cornerstone II, the Partnership and

Cornerstone IV were closed to new investors; Units have been sold

since then solely in "Exchanges" with existing investors, at 100%

of Net Asset Value per Unit.  DWR has been paying all expenses in

connection with the offering of Units since September  30,  1994,

without reimbursement.





Item 6.  Exhibits and Reports on Form 8-K

     A)  Exhibits - None.

     B)  Reports on Form 8-K. - None.





















<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 13, 1999            By: /s/ Lewis A. Raibley, III
                                   Lewis A. Raibley, III
                                    Director  and 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.