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 period ended March 31, 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

                         March 31, 1999
<CAPTION>

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

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

   Statements of Operations for the Quarters Ended
   March 31, 1999 and 1998 (Unaudited)........................3

   Statements of Changes in Partners' Capital for the
   Quarters Ended March 31, 1999 and 1998 (Unaudited).........4

   Statements of Cash Flows for the Quarters Ended
   March 31, 1999 and 1998 (Unaudited)........................5

   Notes to Financial Statements (Unaudited)...............6-10

Item 2. Management's Discussion and Analysis of Financial

Condition and Results of Operations.............. 11-17

Item 3. Quantitative and Qualitative Disclosures about
        Market Risk . . . . . . . . . . . . . . . . . . . 17-29

PART II.                                   OTHER INFORMATION

Item 1. Legal Proceedings.................................   30

Item 2. Changes in Securities and Use of Proceeds.........30-31

Item 6. Exhibits and Reports on Form 8-K.....................31











</TABLE>



<PAGE>
<TABLE>



                 PART I.  FINANCIAL INFORMATION
                                
Item 1.  Financial Statements
                DEAN WITTER CORNERSTONE FUND III
               STATEMENTS OF FINANCIAL CONDITION

<CAPTION>

                                     March 31,     December 31,
                                       1999            1998
                                         $              $
                                    (Unaudited)
ASSETS
<S>                                     <C>            <C>
Equity in futures interests trading accounts:
 Cash                             36,701,618     38,504,975
 Net unrealized gain on open contracts  649,464   2,102,810
 Net option premiums                  (74,375)       (50,047)

      Total Trading Equity        37,276,707     40,557,738

 Interest receivable (DWR)           114,342        120,465
 Due from DWR                         75,007           81,647

      Total Assets                37,466,056     40,759,850

LIABILITIES AND PARTNERS' CAPITAL

Liabilities

 Redemptions payable                289,838         220,184
 Accrued management fees            124,063         135,067
 Accrued administrative expenses     123,192          104,780

      Total Liabilities               537,093         460,031

Partners' Capital

 Limited Partners (11,858.359 and
  12,193.413 Units, respectively) 36,491,670    39,835,572
 General Partner (142.103 Units)      437,293        464,247

 Total Partners' Capital          36,928,963    40,299,819

  Total  Liabilities and Partners' Capital    37,466,056     40,7
59,850


NET ASSET VALUE PER UNIT            3,077.30        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 March 31,

                                       1999            1998
                                        $            $
REVENUES
<S>                           <C>            <C>
 Trading profit (loss):
    Realized                        (264,935)  3,312,479
    Net change in unrealized      (1,453,346)    (307,009)

      Total Trading Results       (1,718,281)  3,005,470

    Interest Income (DWR)           343,469      430,094

      Total Revenues              (1,374,812)   3,435,564


EXPENSES

      Brokerage   commissions  (DWR)       494,855        556,591
Management    fees                        383,211         418,738
Transaction   fees   and  costs             45,762         56,265
Administrative expenses              18,412         13,542
      Total Expenses                942,240      1,045,136

NET INCOME (LOSS)                 (2,317,052)    2,390,428

NET INCOME (LOSS) ALLOCATION:
    Limited Partners              (2,290,098)    2,323,110
    General Partner                  (26,954)       67,318


NET INCOME (LOSS) PER UNIT:
    Limited Partners                 (189.67)       176.18
    General Partner                  (189.67)       176.18

<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 Quarters Ended March 31, 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

Net Income                -       2,323,110     67,3182,390,428

Redemptions               (261.278)      (798,899)              -
(798,899)

Partners' Capital
    March 31, 1998     13,473.159   $41,494,750    $1,211,153 $42
,705,903




Partners' Capital
   December 31, 1998     12,335.516$39,835,572  $464,247$40,299,8
19

Net Loss                 -        (2,290,098) (26,954)(2,317,052)

Redemptions                 (335.054)    (1,053,804)            -
(1,053,804)

Partners' Capital
    March 31, 1999     12,000.462  $36,491,670    $437,293 $36,92
8,963








<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 Quarters Ended March 31,

                                       1999            1998
                                        $            $
CASH FLOWS FROM OPERATING ACTIVITIES
<S>                         <C>              <C>
 Net income (loss)                (2,317,052)  2,390,428
 Noncash item included in net income (loss):
    Net change in unrealized      1,453,346      307,009
 (Increase) decrease in operating assets:
      Net   option  premiums               24,328       (131,265)
Interest   receivable   (DWR)               6,123           1,306
Due from DWR                          6,640       45,073
 Increase (decrease) in operating liabilities:
    Accrued management fees          (11,004)      4,580
    Accrued administrative expenses      18,412      13,542

 Net cash provided by (used for) operating activities   (819,207)
2,630,673


CASH FLOWS FROM FINANCING ACTIVITIES

 Increase (decrease) in redemptions payable69,654  (217,614)
 Redemptions of units             (1,053,804)    (798,899)

 Net cash used for financing activities    (984,150) (1,016,513)

 Net increase (decrease) in cash  (1,803,357)  1,614,160
 Balance at beginning of period   38,504,975    39,762,715

 Balance at end of period        36,701,618    41,376,875


<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 advisors to the  Partnership

are  Abraham  Trading  Co.,  Welton  Investment  Corporation  and

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

Advisors").

                                

                                

                                

<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 has elected to adopt the provisions of SFAS  No.  133

beginning with the fiscal year 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  $649,464  and

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

Of  the  $649,464 net unrealized gain on open contracts at  March

31, 1999, $585,811 related to exchange-traded futures and futures-

styled  option  contracts  and $63,653 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 March 31, 1999 and December 31, 1998 mature

through March 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

March 31, 1999 and December 31, 1998 mature through June 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

$37,287,429  and $40,755,289 at March 31, 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 Ended March 31, 1999

For  the  quarter ended March 31, 1999, the Partnership  recorded

total  trading  losses net of interest income of  $1,374,812  and

posted  a  decrease  in  Net  Asset Value  per  Unit.   The  most

significant 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

<PAGE>

increase during February amid growing speculation that a rise  in

Japanese bond yields would result in Japanese investors replacing

international  bonds with yen-denominated debt.   In  currencies,

losses  were  incurred from long Japanese yen  positions  as  the

value  of  the  yen, despite reaching a 27-month  high  in  early

January,   reversed  sharply  lower  after  the  Bank  of   Japan

intervened in an effort to keep Japanese exports affordable.  The

yen continued to move lower versus the dollar during late January

and  throughout  February  on concerns  regarding  the  Brazilian

economy,  strong  economic data out of  the  U.S.  and  following

comments by key Tokyo officials that Japanese policy makers  were

satisfied  with a weaker yen.  In metals, losses were experienced

during  the  first  half  of March from  short  aluminum  futures

positions  as  prices  increased  amid  a  possible  drawdown  in

warehouse stocks and reports of increased global demand.  Smaller

losses  were  recorded in global stock index futures during  mid-

March  from  long  futures positions in the Financial  Times  100

Index  as  British equity prices slipped following  the  Bank  of

England's  Monetary  Policy  Committee  decision  to  keep  rates

unchanged.  A portion of the Partnership's overall losses for the

quarter were offset by gains recorded in the energy markets  from

long futures positions in crude oil as oil prices climbed on news

that both OPEC and non-OPEC countries had reached an agreement to

cut  total  output  beginning  April  1st.   Smaller  gains  were

recorded in the agricultural markets from short futures positions

in  soybean  and  soybean products as prices declined  due  to  a

healthy  South  American crop, fears that  Brazil  will  increase

exports to support its economy and a continued decline in world

<PAGE>

demand.  Total expenses for the three months ended March 31, 1999

were  $942,240, resulting in a net loss of $2,317,052.  The value

of  a Unit decreased from $3,266.97 at December 1998 to $3,077.30

at March 31, 1999.

For the Quarter Ended March 31, 1998

For  the  quarter ended March 31, 1998, the Partnership  recorded

total  trading  revenues including interest income of  $3,435,564

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

significant gains were recorded from long U.S. and European stock

index  futures  positions  as prices  in  these  markets  trended

consistently  higher throughout the quarter.  Additional  profits

were recorded from long European bond futures positions as prices

in  these  markets also trended higher during  the  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.  Smaller gains were  recorded

from  short  positions in livestock futures as  prices  in  these

markets  moved lower during February.  These gains were partially

offset  by losses experienced in metals 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  as

the  value  of  the  Australian dollar and  British  pound  moved

without  consistent  direction  throughout  a  majority  of   the

quarter.   Total  expenses for the three months ended  March  31,

1998 were $1,045,136, resulting in net income of $2,390,428.  The

value of

                                

<PAGE>

a Unit increased from $2,993.52 at December 31, 1997 to $3,169.70

at March 31, 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

Partnership  has a material relationship - the futures  exchanges

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

<PAGE>

     Trading Advisors - 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

Advisors throughout 1999 in their Year 2000 compliance and, where

applicable,  to  test its external interface with  Carr  and  the

Trading Advisors.

      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

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

<PAGE>

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

to the euro prevents the Trading Advisors 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

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.

                                

<PAGE>

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 quantitative disclosures in this section  are

deemed to be forward-looking statements for purposes of the  safe

harbor, except for statements of historical fact.





<PAGE>

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 Advisors 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 Partnership's VaR, the historical

observation   period   is   approximately   four   years.     The

Partnership's one-day 99% VaR

                                

<PAGE>

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 Advisors 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 March 31, 1999.  As of March 31,  1999,

the  Partnership's  total capitalization  was  approximately  $37

million.

     Primary Market             March 31, 1999
     Risk Category              Value at Risk

     Interest Rate                 (0.43)%

     Currency                      (1.37)

     Equity                        (0.50)

      Commodity                         (0.79)

      Aggregate Value at Risk      (1.99)%







                                

<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   March  31,  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 April  1,

1998 through March 31, 1999.

Primary Market Risk Category        High      Low      Average

Interest Rate                      (1.74)%   (0.43)%   (1.15)%

Currency                           (1.37)    (0.72)    (1.00)

Equity                             (0.91)    (0.08)    (0.53)

Commodity                          (0.93)    (0.68)    (0.78)

Aggregate Value at Risk            (2.23)%   (1.61)%   (1.88)%




<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 March 31, 1999 and for the  end  of  the  four

quarterly  reporting periods from April 1, 1998 through  March  31,

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

90%)  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  Advisors

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 March 31, 1999, by market sector.   It  may  be

anticipated  however,  that  these  market  exposures  will  vary

materially over time.

      Interest Rate.  Interest rate risk is the principal  market

exposure  of  the  Partnership. Interest rate movements  directly

affect the price of the sovereign bond futures positions held by

<PAGE>

the  Partnership and indirectly 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 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.  New  Zealand  and

Australia.



Demeter  anticipates  that G-7 interest  rates  will  remain  the

primary  market  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  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.   These  fluctuations  are  influenced   by

interest  rate changes as well as political and general  economic

conditions.   The  Partnership  trades  in  a  large  number   of

currencies, including cross-rates - i.e., positions between two

                                

<PAGE>

currencies   other   than   the  U.S.   dollar.    However,   the

Partnership's  major  exposures  have  typically  been   in   the

dollar/yen, dollar/mark, dollar/euro and dollar/pound  positions.

Demeter  does  not  anticipate  that  the  risk  profile  of  the

Partnership's  currency sector will change significantly  in  the

future,  although it is difficult at this point  to  predict  the

effect  of  the introduction of the Euro on the Trading Advisors'

currency trading strategies.

       Equity.  The Partnership's  primary equity exposure is  to

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

traded  by  the  Partnership are by law  limited  to  futures  on

broadly  based  indices.  As of March 31, 1999, the Partnership's

primary  exposures  were  in  the  S&P  500  and  All  Ordinaries

(Australia) stock indices.  Demeter anticipates little,  if  any,

trading  in non-G-7 stock indices.  The Partnership is  primarily

exposed to the risk of adverse price trends or static markets  in

the  major 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).

     Commodity.

    Metals.  The Partnership's primary metals market exposure  is

to  fluctuations  in  the  price of gold  and  silver.   Although

certain Trading Advisors will from time to time trade base metals

such  as aluminum, copper, nickel and zinc, the principal  market

exposures  of  the  Partnership have  consistently  been  in  the

precious metals, gold and silver (and, to a much lesser extent,

<PAGE>

platinum and palladium).  The Trading Advisors' 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 Advisors 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.

      Soft  Commodities and Agriculturals. One  of  the  Partner-

ship's  primary  commodities exposure is to fluctuations  in  the

price  of  agriculturals and soft commodities,  which  are  often

directly  affected  by severe or unexpected  weather  conditions.

Soybeans,  sugar and corn accounted for the substantial  bulk  of

the Partnership's commodities exposure at March 31, 1999.  In the

past  the  Partnership has had material market exposure  to  live

cattle  and lean hogs, currently does and may do so again in  the

future.   However, Demeter anticipates that the Trading  Advisors

will  maintain an emphasis on soybeans, sugar and corn, in  which

the Partnership has historically taken it's largest positions.

     Energy.  The Partnership's primary energy market exposure is

to  gas  and oil price movements, often resulting from  political

developments  in the Middle East.  Although the Trading  Advisors

trade natural gas to a limited extent, oil is by far the dominant

energy  market  exposure  of  the Partnership.   Oil  prices  are

currently  depressed,  but they can be volatile  and  substantial

profits and losses have been and are expected to continue  to  be

experienced in this market.



<PAGE>

Qualitative Disclosures Regarding Non-Trading Risk Exposure

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

Partnership at March 31, 1999.



Foreign  Currency  Balances.  The Partnership's  primary  foreign

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

Mexican  pesos and Australian dollars.  The Partnership  controls

the  non-trading  risk of these balances by regularly  converting

these  balances  back  into U.S. dollars  at  varying  intervals,

depending upon such factors as size, volatility, etc.



Qualitative Disclosures Regarding Means of Managing Risk Exposure

The  means  by  which the Partnership and the  Trading  Advisors,

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  Advisors, each of whose strategies  focus  on

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

monitoring  the performance of the Trading Advisors  on  a  daily

basis.     In    addition,   the   Trading   Advisors   establish

diversification  guidelines, often set in terms  of  the  maximum

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

market  sensitive instrument.  One should be aware  that  certain

Trading  Advisors  treat their risk control  policies  as  strict

rules, whereas others treat such policies as general guidelines.

                                

<PAGE>

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 Advisors.



















































<PAGE>
                   PART II.  OTHER INFORMATION

                                

Item 1.   LEGAL PROCEEDINGS

The  following supplements Legal Proceedings previously disclosed

in Item 3. of the Partnership's  1998 Form 10-K:



On  April  12,  1999,  the  defendants  filed  a  motion  in  the

California  action to oppose certification by the  court  of  the

class in the California litigation.



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

April 1, 1999. Through April 1, 1999, an aggregate of 235,422.053



<PAGE>

Units  have been sold leaving 14,577.947 Units remaining  available

for sale as of April 1, 1999.



The  aggregate  price of Units sold through April  1,  1999  with

respect to Cornerstone III is $137,132,762.



Effective September 30, 1984, Cornerstone II, Cornerstone III 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)

May 14, 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.