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 March 31, 2004 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 No. 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.)

Demeter Management Corporation
825 Third Avenue, 9th Floor
New York, NY                                          10022
(Address of principal executive offices)	  	      (Zip Code)

Registrant's telephone number, including area code (212) 310-6444













(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___________


Indicate by check-mark whether the registrant is an accelerated
filer (as defined in Rule 12b-2 of the Exchange Act).

Yes            No    X


<page> <table>	DEAN WITTER CORNERSTONE FUND III

	INDEX TO QUARTERLY REPORT ON FORM 10-Q

	March 31, 2004

<caption>



PART I. FINANCIAL INFORMATION

				<c>
Item 1. Financial Statements

		Statements of Financial Condition as of March 31, 2004
		(Unaudited) and December 31, 2003..........................2

		Statements of Operations for the Quarters Ended
		March 31, 2004 and 2003 (Unaudited)........................3

		Statements of Changes in Partners' Capital for the
		Quarters Ended March 31, 2004 and 2003 (Unaudited)........ 4

		Statements of Cash Flows for the Quarters Ended
		March 31, 2004 and 2003 (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.........................................18-31

Item 4.	Controls and Procedures................................31


Part II. OTHER INFORMATION

Item 1.	Legal Proceedings......................................32

Item 6.	Exhibits and Reports on Form 8-K....................32-34
</table>


<page> <table> PART I.  FINANCIAL INFORMATION

Item 1.  Financial Statements

	DEAN WITTER CORNERSTONE FUND III
	STATEMENTS OF FINANCIAL CONDITION

	                     March 31,	December  31,
	      2004     	      2003
	                      $	   $
	                     (Unaudited)
ASSETS

	<c>	<c>
Equity in futures interests trading accounts:
	Cash	30,256,375	25,869,355

	Net unrealized gain on open contracts (MS&Co.)	1,514,537	1,572,599
	Net unrealized gain on open contracts (MSIL)	    608,993	    889,391

	     Total net unrealized gain on open contracts	  2,123,530	   2,461,990

	     Total Trading Equity	32,379,905	28,331,345

Interest receivable (Morgan Stanley DW)	        20,226	        16,293

	     Total Assets	  32,400,131	  28,347,638

LIABILITIES AND PARTNERS' CAPITAL

Liabilities

Redemptions payable	321,763	119,105
Accrued administrative expenses	132,894	149,518
Accrued management fees	       94,113	         82,245

	     Total Liabilities	      548,770	       350,868

Partners' Capital

Limited Partners (6,895.866 and
	  7,059.053 Units, respectively)	31,384,785	27,596,004
General Partner (102.516 Units)		      466,576	      400,766

	     Total Partners' Capital	   31,851,361	  27,996,770

	     Total Liabilities and Partners' Capital	  32,400,131	  28,347,638


NET ASSET VALUE PER UNIT	       4,551.25	      3,909.31


<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,

	      2004     	      2003
	      $	      $
REVENUES

			<c>	<c>
	Trading profit (loss):
		Realized	5,468,312	4,713,688
		Net change in unrealized	   (338,460)	 (2,541,129)

			Total Trading Results 	5,129,852	2,172,559

	Interest income (Morgan Stanley DW)	       56,794	      70,514

			Total	   5,186,646	 2,243,073

EXPENSES
	Brokerage commissions (Morgan Stanley DW)		307,881	378,565
	Management fees		272,081	270,274
	Common administrative expenses	19,000	     25,038
	Transaction fees and costs		    13,318	    21,174

			Total		   612,280	    695,051


NET INCOME 	 4,574,366	  1,548,022


NET INCOME ALLOCATION

	Limited Partners                                                                           4,508,556		1,520,037
	General Partner                                                                             	65,810	27,985


NET INCOME PER UNIT

	Limited Partners	     641.94		196.95
	General Partner	     641.94		196.95


<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, 2004 and 2003
	(Unaudited)

<caption>



                                                                          Units of
	Partnership	Limited	General
	     Interest   	  Partners  	   Partner   	     Total
		$	$	$



	<c>	<c>	<c>	<c>
Partners' Capital,
December 31, 2002	7,750.175	27,329,760	510,464	27,840,224

Net Income	-	1,520,037	27,985	1,548,022

Redemptions	   (203.891)	   (644,177) 	 (150,000) 	 (794,177)

Partners' Capital,
March 31, 2003	   7,546.284	28,205,620	             388,449	28,594,069






Partners' Capital,
December 31, 2003	7,161.569	27,596,004	400,766	27,996,770

Net Income	-	4,508,556	65,810	4,574,366

Redemptions	   (163.187)	   (719,775) 	         -     	       (719,775)

Partners' Capital,
March 31, 2004	   6,998.382	31,384,785	             466,576	  31,851,361




<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,

	      2004     	      2003
	    $	      $


CASH FLOWS FROM OPERATING ACTIVITIES

			<c>	<c>
Net income 	4,574,366		1,548,022
Noncash item included in net income:
	Net change in unrealized	   338,460		2,541,129

(Increase) decrease in operating assets:
	Interest receivable (Morgan Stanley DW)	     (3,933)		(1,622)
	Due from Morgan Stanley DW                                                            -		229,448

Increase (decrease) in operating liabilities:
	Accrued administrative expenses	   (16,624)		(7,260)
	Accrued management fees                                                           11,868		           3,237

Net cash provided by operating activities                                     4,904,137	  	      4,312,954


CASH FLOWS FROM FINANCING ACTIVITIES

Increase in redemptions payable	202,658		352,791
Redemptions of Units                                                                   (719,775)		 (794,177)

Net cash used for financing activities                                           (517,117)		(441,386)

Net increase in cash                                                                    4,387,020		3,871,568

Balance at beginning of period                                                  25,869,355		 26,372,589

Balance at end of period                                                           30,256,375		 30,244,157



<fn>


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

</table>


<page> DEAN WITTER CORNERSTONE FUND III
NOTES TO FINANCIAL STATEMENTS
March 31, 2004
(Unaudited)


The unaudited financial statements contained herein 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, 2003 Annual Report
on Form 10-K.

1.  Organization
Dean Witter Cornerstone Fund III is a New York limited partnership
organized to engage in the speculative trading of futures
contracts, options on futures contracts and forward contracts on
foreign currencies and other commodity interests. The Partnership
is one of the Dean Witter Cornerstone Funds, comprised of the
Partnership, Dean Witter Cornerstone Fund II and Dean Witter
Cornerstone Fund IV.

The Partnership's general partner is Demeter Management
Corporation ("Demeter"). The non-clearing commodity broker is
Morgan Stanley DW Inc. ("Morgan Stanley DW").  The clearing
commodity brokers are Morgan Stanley & Co. Incorporated ("MS &
Co.") and Morgan Stanley & Co. International Limited ("MSIL").
<page> DEAN WITTER CORNERSTONE FUND III
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
Demeter, Morgan Stanley DW, MS & Co. and MSIL are wholly-owned
subsidiaries of Morgan Stanley.  The trading managers to the
Partnership are Graham Capital Management, L.P. and Sunrise
Capital Management, Inc. (individually, a "Trading Manager", or
collectively, the "Trading Managers").

2.  Related Party Transactions
The Partnership's cash is on deposit with Morgan Stanley DW, MS &
Co. and MSIL in futures, forwards and options trading accounts to
meet margin requirements as needed. Morgan Stanley DW pays
interest on these funds based on a rate equal to the average yield
on 13-week U.S. Treasury bills. The Partnership pays brokerage
commissions to Morgan Stanley DW.

3.  Financial Instruments
The Partnership trades futures contracts, options on futures
contracts 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.

<page> DEAN WITTER CORNERSTONE FUND III
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
The market value of contracts is based on closing prices quoted
by the exchange, bank or clearing firm through which the
contracts are traded.

The Partnership's contracts are accounted for on a trade-date
basis and marked to market on a daily basis. The Partnership
accounts for its derivative investments in accordance with the
provisions of Statement of Financial Accounting Standards No.
133, "Accounting for Derivative Instruments and Hedging
Activities" ("SFAS No. 133").  SFAS No. 133 defines a derivative
as a financial instrument or other contract that has all three of
the following characteristics:

1)	One or more underlying notional amounts or payment
provisions;
2)	Requires no initial net investment or a smaller initial net
investment than would be required relative to changes in
market factors;
3)	Terms require or permit net settlement.

Generally, derivatives include futures, forward, swaps or options
contracts, and other financial instruments with similar
characteristics such as caps, floors and collars.


<page> DEAN WITTER CORNERSTONE FUND III
NOTES TO FINANCIAL STATEMENTS (CONTINUED)
The net unrealized gains (losses) on open contracts, reported as a
component of "Equity in futures interests trading accounts" on the
statements of financial condition, and their longest contract
maturities were as follows:

	Net Unrealized Gains (Losses)
	on Open Contracts	Longest Maturities
		Off-			Off-
	Exchange-	Exchange-		Exchange-	Exchange-
Date	 Traded  	  Traded   	Total	 Traded  	 Traded
	 $	  $	$

Mar. 31, 2004 	2,203,292	(79,762)	2,123,530	Sep. 2005	Jun. 2004
Dec. 31, 2003	2,061,496	400,494	2,461,990	Jun. 2005	Mar. 2004

The Partnership has 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.



The Partnership also has credit risk because Morgan Stanley DW, MS
& Co. and MSIL 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. Morgan Stanley DW, MS & Co., and MSIL,
each as a futures commission merchant for the Partnership's
exchange-traded futures and futures-styled options contracts, are
required, pursuant to regulations of the Commodity Futures Trading
<page> DEAN WITTER CORNERSTONE FUND III
NOTES TO FINANCIAL STATEMENTS (CONCLUDED)

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
gains (losses) on all open futures and futures-styled options
contracts, which funds, in the aggregate, totaled $32,459,667
and $27,930,851 at March 31, 2004 and December 31, 2003,
respectively. With respect to the Partnership's off-exchange-
traded forward currency contracts, there are no daily exchange-
required settlements of variations in value nor is there any
requirement that an amount equal to the net unrealized gains
(losses) on open forward contracts be segregated, however, MS &
Co. and Morgan Stanley DW will make daily settlements of losses as
needed.  With respect to those off-exchange-traded forward
currency contracts, the Partnership is at risk to the ability of
MS & Co., the sole counterparty on all such contracts, to perform.
The Partnership has a netting agreement with MS & Co.  This
agreement, which seeks to reduce both the Partnership's and MS &
Co.'s exposure on off-exchange-traded forward currency contracts,
should materially decrease the Partnership's credit risk in the
event of MS & Co.'s bankruptcy or insolvency.


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


Liquidity.  The Partnership deposits its assets with Morgan
Stanley DW as non-clearing broker, and MS & Co. and MSIL as
clearing brokers in separate futures, forwards and options trading
accounts established for each Trading Manager, which assets are
used as margin to engage in trading and may be used as margin
solely for the Partnership's trading. The assets are held in
either non-interest bearing bank accounts or in securities and
instruments permitted by the CFTC for investment of customer
segregated or secured funds.  Since the Partnership's sole purpose
is to trade in futures, forwards and options, it is expected that
the Partnership will continue to own such liquid assets for margin
purposes.

The Partnership's investment in futures, forwards, and options
may, from time to time, be illiquid.  Most U.S. futures exchanges
limit fluctuations in prices during a single day by regulations
referred to as "daily price fluctuations limits" or "daily
limits".  Trades may not be executed at prices beyond the daily
limit.  If the price for a particular futures or options contract
has increased or decreased by an amount equal to the daily limit,
positions in that futures or options contract can neither be taken
nor liquidated unless traders are willing to effect trades at or
within the limit. Futures prices have occasionally moved the daily
limit for several consecutive days with little or no trading.
<page> These market conditions could prevent the Partnership from
promptly liquidating its futures or options contracts and result
in restrictions on redemptions.

There is no limitation on daily price moves in trading forward
contracts on foreign currencies.  The markets for some world
currencies have low trading volume and are illiquid, which may
prevent the Partnership from trading in potentially profitable
markets or prevent the Partnership from promptly liquidating
unfavorable positions in such markets, subjecting it to
substantial losses.  Either of these market conditions could
result in restrictions on redemptions.  For the periods covered by
this report, illiquidity has not materially affected the
Partnership's assets.

There are no known material trends, demands, commitments, events
or uncertainties at the present time that will result in, or that
are reasonably likely to result in, the Partnership's liquidity
increasing or decreasing in any material way.

Capital Resources.  The Partnership does not have, nor expect to
have, any capital assets.  Redemptions of additional units of
limited partnership interest ("Unit(s)") in the future will affect
the amount of funds available for investment in futures, forwards
and options in subsequent periods.  It is not possible to estimate
<page> the amount, and therefore the impact, of future redemptions
of Units.

There are no known material trends, favorable or unfavorable, that
would affect, nor any expected material changes to, the
Partnership's capital resource arrangements at the present time.
The Partnership does not have any off-balance sheet arrangements,
nor does it have contractual obligations or commercial commitments
to make future payments that would affect its liquidity or capital
resources.

Results of Operations
General.  The Partnership's results depend on the Trading Managers
and the ability of each Trading Manager's trading programs to take
advantage of price movements or other profit opportunities in the
futures, forwards and options markets.  The following presents a
summary of the Partnership's operations for the three month
periods ended March 31, 2004 and 2003, and a general discussion of
its trading activities during each period.  It is important to
note, however, that the Trading Managers trade in various markets
at different times and that prior activity in a particular market
does not mean that such market will be actively traded by the
Trading Managers or will be profitable in the future.
Consequently, the results of operations of the Partnership are
difficult to discuss other than in the context of the Trading
Managers' trading activities on behalf of the Partnership and how
<page> the Partnership has performed in the past. Past performance
is not necessarily indicative of future results.

The Partnership's results of operations set forth in the financial
statements on pages 2 through 10 of this report were prepared in
accordance with accounting principles generally accepted in the
United States of America, which require the use of certain
accounting policies that affect the amounts reported in these
financial statements, including the following:  The contracts the
Partnership trades are accounted for on a trade-date basis and
marked to market on a daily basis.  The difference between their
cost and market value is recorded on the Statements of Operations
as "Net change in unrealized profit/loss" for open (unrealized)
contracts, and recorded as "Realized profit/loss" when open
positions are closed out, and the sum of these amounts constitutes
the Partnership's trading revenues.  The market value of a futures
contract is the settlement price on the exchange on which that
futures contract is traded on a particular day. The value of
foreign currency forward contracts is based on the spot rate as of
the close of business, New York City time, on a given day.
Interest income revenue, as well as management fees, incentive
fees and brokerage commissions expenses of the Partnership are
recorded on an accrual basis.

Demeter believes that, based on the nature of the operations of
the Partnership, no assumptions relating to the application of
<page> critical accounting policies other than those presently
used could reasonably affect reported amounts.

For the Quarter Ended March 31, 2004
The Partnership recorded revenues including interest income
totaling $5,186,646 and expenses totaling $612,280, resulting in
net income of $4,574,366 for the quarter ended March 31, 2004.
The Partnership's net asset value per Unit increased from
$3,909.31 at December 31, 2003 to $4,551.25 at March 31, 2004.

The most significant trading gains of approximately 6.8% were
recorded in the metals markets.  Long futures positions in base
metals, such as copper and aluminum, supplied gains as lower
supply and heightened demand from Asia caused prices to increase.
During March, long futures positions in silver benefited as
prices consistently moved higher amid central bank demand
triggered by lower currency values.  Additional gains of
approximately 4.6% were recorded in the global interest rate
markets from long positions in European and U.S. interest rate
futures.  Bond prices benefited from the January release of weak
U.S. economic data and February comments from global central
banks regarding non-inflationary economic environments that did
not warrant an increase in interest rates.  Profits of
approximately 2.3% were recorded in the energy markets, primarily
during February, from long futures positions in crude oil and its
related products as low market supply, falling inventory levels
<page> and production cut announcements from OPEC caused prices
to increase.  In the agricultural markets, gains of approximately
2.1% were generated from long futures positions in soybeans,
soybean-related products and corn.  Growing U.S. exports and
heightened demand from Asia pushed prices for these commodities
higher during the quarter.  Further Partnership's overall gains
of approximately 1.4% were achieved in the global stock index
markets.  During March, long positions in Japanese stock index
futures returned gains as Japanese equity prices rallied higher
in response to positive economic data that reflected the steady
pace of Japan's economic recovery.  During January, long
positions in U.S. stock index futures provided gains as prices
rallied on reports of strong company earnings.  A portion of the
Partnership's overall gains for the quarter was offset by losses
of approximately 0.4% in the currency sector.  The majority of
the sector losses were incurred during March from short Japanese
yen positions against the U.S. dollar as the value of the yen
reversed higher due to speculation that the Bank of Japan was
relaxing its efforts to weaken the Japanese currency.

For the Quarter Ended March 31, 2003
The Partnership recorded revenues including interest income
totaling $2,243,073 and expenses totaling $695,051, resulting in
net income of $1,548,022 for the quarter ended March 31, 2003.
The Partnership's net asset value per Unit increased from
$3,592.21 at December 31, 2002 to $3,789.16 at March 31, 2003.
<page> The most significant trading gains of approximately 4.4%
were recorded in the energy markets during January and February
from long positions in natural gas futures as prices increased
sharply due to prolonged frigid temperatures in the northeastern
and midwestern U.S.  Elsewhere in the energy markets, long
positions in crude oil futures resulted in gains as prices
trended higher during January and February amid the looming
threat of a Coalition-led war against Iraq and an overall decline
in inventories.  Additional gains of approximately 1.3% were
recorded in the global interest rate markets from long positions
in European and U.S. interest rate futures as prices trended
higher during January and February as investors continued to seek
the safe haven of fixed income investments in response to
continued uncertainty in the global equity markets.  Smaller
gains of approximately 1.2% were recorded in the currency markets
from long positions in the euro and Swiss franc versus the U.S.
dollar as the value of these European currencies strengthened
amid the release of weak U.S. economic data and fear of military
action against Iraq.  A portion of the Partnership's overall
gains was offset by losses of approximately 0.9% incurred in the
metals markets primarily during March from long positions in
aluminum and copper futures as prices reversed sharply lower due
to muted industrial demand.


<page> Item 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT
MARKET RISK

Introduction
The Partnership is a commodity pool engaged primarily in the
speculative trading of futures, forwards and options.  The market-
sensitive instruments held by the Partnership are acquired for
speculative trading purposes only and, as a result, all or
substantially all of the Partnership's assets are at risk of
trading loss.  Unlike an operating company, the risk of market-
sensitive instruments is inherent to the primary business activity
of the Partnership.

The futures, forwards and options traded by the Partnership
involve varying degrees of related market risk.  Market risk is
often dependent upon changes in the level or volatility of
interest rates, exchange rates, and prices of financial
instruments and commodities, factors that result in frequent
changes in the fair value of the Partnership's open positions,
and consequently in its earnings, whether realized or unrealized,
and cash flow.  Profits and losses on open positions of exchange-
traded futures, forwards and options are settled daily through
variation margin.

The Partnership's total market risk may increase or decrease as
it is influenced by a wide variety of factors, including, but not
limited to, the diversification among the Partnership's open
<page> positions, the volatility present within the markets, and
the liquidity of the markets.

The Partnership's past performance is not necessarily indicative
of its future results.  Any attempt to numerically quantify the
Partnership's market risk is limited by the uncertainty of its
speculative trading.  The Partnership's speculative trading may
cause future losses and volatility (i.e., "risk of ruin") that
far exceed the Partnership's experience to date or any reasonable
expectations based upon historical changes in market value.

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.

The Partnership accounts for open positions on the basis of mark
to market accounting principles.  Any loss in the market value of
the Partnership's open positions is directly reflected in the
Partnership's earnings and cash flow.
<page> The Partnership's risk exposure in the market sectors
traded by the Trading Managers is estimated below in terms of
Value at Risk ("VaR"). The Partnership estimates VaR using a
model based upon historical simulation (with a confidence level
of 99%) which involves constructing a distribution of
hypothetical daily changes in the value of a trading portfolio.
The VaR model takes into account linear exposures to risk
including equity and commodity prices, interest rates, foreign
exchange rates, and correlation among these variables. The
hypothetical changes in portfolio value are based on daily
percentage changes observed in key market indices or other market
factors ("market risk factors") to which the portfolio is
sensitive.  The one-day 99% confidence level of the Partnership's
VaR corresponds to the negative change in portfolio value that,
based on observed market risk factors, would have been exceeded
once in 100 trading days, or one day in 100.  VaR typically does
not represent the worst case outcome.  Demeter uses approximately
four years of daily market data (1,000 observations) and revalues
its portfolio (using delta-gamma approximations) for each of the
historical market moves that occurred over this time period.
This generates a probability distribution of daily "simulated
profit and loss" outcomes.  The VaR is the appropriate percentile
of this distribution.  For example, the 99% one-day VaR would
represent the 10th worst outcome from Demeter's simulated profit
and loss series.

<page> The Partnership's VaR computations are based on the risk
representation of the underlying benchmark for each instrument or
contract and do not distinguish between exchange and non-exchange
dealer-based instruments. They are also not based on exchange
and/or dealer-based maintenance margin requirements.

VaR models, including the Partnership's, are continually evolving
as trading portfolios become more diverse and modeling techniques
and systems capabilities improve.  Please note that the VaR model
is used to numerically 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.
Please further note that VaR as described above may not be
comparable to similarly titled measures used by other entities.

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 primary market risk category at March 31, 2004 and 2003. At
March 31, 2004 and 2003, the Partnership's total capitalization
was approximately $32 million and $29 million, respectively.











<page>
Primary Market	               March 31, 2004      March 31, 2003
Risk Category	                Value at Risk       Value at Risk

Interest Rate	(2.18)%	(0.71)%
Equity   	(0.70)	(0.78)
Currency   	(0.24)	(0.92)
Commodity                     	(1.25)	(0.47)
Aggregate Value at Risk           (2.42)%	(1.54)%

The VaR for a market category represents the one-day downside risk
for the aggregate exposures associated with this market category.
The Aggregate Value at Risk listed above represents the VaR of the
Partnership's open positions across all the market categories, and
is less than the sum of the VaRs for all such market categories
due to the diversification benefit across asset classes.

Because the business of the Partnership is the speculative
trading of futures, forwards and options, the composition of its
trading portfolio can change significantly over any given time
period, or even within a single trading day, which could
positively or negatively materially impact market risk as
measured by VaR.

The table below supplements the quarter-end VaR set forth above
by presenting the Partnership's high, low and average VaR, as a
percentage of total net assets for the four quarter-end reporting
periods from April 1, 2003 through March 31, 2004.
<page>
Primary Market Risk Category	High	Low	Average
Interest Rate	(2.18)%	(0.33)%	(1.11)%

Equity	(2.23)	(0.70)	(1.38)

Currency	(1.46)	(0.24)	(1.05)

Commodity	(1.73)	(1.25)	(1.49)

Aggregate Value at Risk	    (3.19)%	(2.42)%	(2.70)%


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
requirements.  Margin requirements generally range between 2% and
15% of contract face value. Additionally, the use of leverage
causes the face value of the market sector instruments held by the
Partnership to typically be many times the total capitalization of
the Partnership.  The value of the Partnership's open positions
thus creates a "risk of ruin" not typically found in other
investments.  The relative size of the positions held may cause
the Partnership to incur losses greatly in excess of VaR within a
short period of time, given the effects of the leverage employed
and market volatility.  The VaR tables above, as well as the past
performance of the Partnership, give no indication of such "risk
of ruin". In addition, VaR risk measures should be viewed in light
of the methodology's limitations, which include the following:
?	past changes in market risk factors will not always result in
accurate predictions of the distributions and correlations of
future market movements;
<page>
?	changes in portfolio value caused by market movements may
differ from those of the VaR model;
?	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.

The VaR tables provided 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, 2004 and 2003, and for the four
quarter-end reporting periods from April 1, 2003 through March 31,
2004.  VaR is not necessarily representative of the Partnership's
historic risk, nor should it be used to predict the Partnership's
future financial performance or its ability to manage or monitor
risk.  There can be no assurance that the Partnership's actual
losses on a particular day will not exceed the VaR amounts
indicated above or that such losses will not occur more than once
in 100 trading days.



<page>
Non-Trading Risk
The Partnership has non-trading market risk on its foreign cash
balances not needed for margin.  These balances and any market
risk they may represent are immaterial.

The Partnership also maintains a substantial portion
(approximately 90% as of March 31, 2004) of its available assets
in cash at Morgan Stanley DW.  A decline in short-term interest
rates would result in a decline in the Partnership's cash
management income. This cash flow risk is not considered to be
material.

Materiality, as used throughout this section, is based on an
assessment of reasonably possible market movements and any
associated potential losses, taking into account the leverage,
optionality and multiplier features of the Partnership's market-
sensitive instruments, in relation to the Partnership's net
assets.

Qualitative Disclosures Regarding Primary Trading Risk Exposures
The following qualitative disclosures regarding the Partnership's
market risk exposures - except for (A) those disclosures that are
statements of historical fact and (B) the descriptions of how the
Partnership manages its primary market risk exposures - constitute
forward-looking statements within the meaning of Section 27A of
<page> 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 at March 31, 2004, by market sector.  It may be
anticipated, however, that these market exposures will vary
materially over time.

Interest Rate.  The Partnership's primary market exposure at March
31, 2004 was to the global interest rate sector.  Exposure was
primarily spread across the Japanese, U.S. and European interest
rate sectors.  Interest rate movements directly affect the price
of the sovereign bond futures positions held by the Partnership
<page> 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 interest rate exposure is generally to interest rate
fluctuations in the U.S. and the other G-7 countries.  The G-7
countries consist of France, the U.S., Britain, Germany, Japan,
Italy and Canada.  However, the Partnership also takes futures
positions in the government debt of smaller countries - e.g.,
Australia.  Demeter anticipates that the G-7 countries and
Australian interest rates will remain the primary interest rate
exposures of the Partnership for the foreseeable future.  The
speculative futures positions held by the Partnership may range
from short to long-term instruments.  Consequently, changes in
short, medium or long-term interest rates may have an effect on
the Partnership.

Equity.  The second largest market exposure of the Partnership at
March 31, 2004 was 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.  At March 31, 2004, the
Partnership's primary exposures were to the S&P 500 (U.S.), Nikkei
(Japan) and TOPIX (Japan) stock indices.  The Partnership is
primarily exposed to the risk of adverse price trends or static
markets in the U.S., Japanese and European stock indices.  Static
markets would not cause major market changes but would make it
<page> difficult for the Partnership to avoid trendless price
movements, resulting in numerous small losses.

Currency.  The third largest market exposure of the Partnership at
March 31, 2004 was to the currency sector.  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 a large
number of currencies including cross-rate - i.e., positions
between two currencies other than the U.S. dollar.  At March 31,
2004, the Partnership's major exposures were to the euro and
British pound currency crosses, as well as to outright U.S. dollar
positions.  Outright positions consist of the U.S. dollar vs.
other currencies.  These other currencies include 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 VaR figure includes foreign margin
amounts converted into U.S. dollars with an incremental adjustment
to reflect the exchange rate risk inherent to the U.S.-based
Partnership in expressing VaR in a functional currency other than
U.S. dollars.

Commodity.
<page> Energy. The Partnership's energy exposure at March 31,
2004 was shared primarily by futures contracts in crude oil
and its related products, and natural gas.  Price movements
in these markets result from geopolitical developments,
particularly in the Middle East, as well as weather patterns
and other economic fundamentals.  Significant profits and
losses, which have been experienced in the past, are expected
to continue to be experienced in the future.  Natural gas has
exhibited volatility in price resulting from weather patterns
and supply and demand factors and will likely continue in
this choppy pattern.

Metals.  The Partnership's metals exposure at March 31, 2004
was to fluctuations in the price of precious metals, such as
gold and silver, and base metals, such as copper and
aluminum.  Economic forces, supply and demand inequalities,
geopolitical factors and market expectations influence price
movements in these markets.  The Trading Managers, from time
to time, take positions when market opportunities develop,
and Demeter anticipates that the Partnership will continue to
do so.

Soft Commodities and Agriculturals.  At March 31, 2004, the
Partnership had exposure to the markets that comprise these
sectors.  Most of the exposure was to corn, wheat and cotton.
Supply and demand inequalities, severe weather disruptions
<page> and market expectations affect price movements in
these markets.


Qualitative Disclosures Regarding Non-Trading Risk Exposure
The following was the only non-trading risk exposure of the
Partnership at March 31, 2004:

Foreign Currency Balances.  The Partnership's primary foreign
currency balances at March 31, 2004 were in euros, Japanese
yen and Australian dollars.  The Partnership controls the
non-trading risk of foreign currency balances by regularly
converting them back into U.S. dollars upon liquidation of
their respective positions.

Qualitative Disclosures Regarding Means of Managing Risk Exposure
The Partnership and the Trading Managers, separately, attempt to
manage the risk of the Partnership's open positions in essentially
the same manner in all market categories traded.  Demeter attempts
to manage market exposure by diversifying the Partnership's assets
among different Trading Managers, each of whose strategies focus
on different market sectors and trading approaches, and by
monitoring the performance of the Trading Managers daily.  In
addition, the Trading Managers establish diversification
guidelines, often set in terms of the maximum margin to be <page>
committed to positions in any one market sector or market-
sensitive instrument.

Demeter monitors and controls the risk of the Partnership's non-
trading instrument, cash.  Cash is the only Partnership investment
directed by Demeter, rather than the Trading Managers.

Item 4.	CONTROLS AND PROCEDURES

(a)	As of the end of the period covered by this quarterly
report, the President and Chief Financial Officer of
the general partner, Demeter, have evaluated the
effectiveness of the Partnership's disclosure controls
and procedures (as defined in Rules 13a-15(e) and 15d-
15(e) of the Exchange Act), and have judged such
controls and procedures to be effective.

   (b)	There have been no significant changes in the
Partnership's internal controls or in other factors
that could significantly affect these controls
subsequent to the date of their evaluation.


<page> PART II.  OTHER INFORMATION

Item 1.  LEGAL PROCEEDINGS
None.



Item 6.  EXHIBITS AND REPORTS ON FORM 8-K

(A)	Exhibits

3.01	Limited Partnership Agreement of the Partnership, dated
as of December 7, 1983, as amended as of May 11, 1984, is
incorporated by reference to Exhibit 3.01 of the
Partnership's Annual Report on Form 10-K for the fiscal
year ended September 30, 1984 (File No. 0-13299).
10.01	Management Agreement among the Partnership, Demeter and
Sunrise Capital Management Inc. (formerly Sunrise
Commodities Inc.), dated as of November 15, 1983, is
incorporated by reference to Exhibit 10.03 of the
Partnership's Annual Report on Form 10-K for the fiscal
year ended September 30, 1984 (File No. 0-13299).
10.02	Management Agreement among the Partnership, Demeter and
Welton Investment Systems Corporation, dated as of July
1, 1996, is incorporated by reference to Exhibit 10.02 of
the Partnership's Annual Report on Form 10-K for the
fiscal year ended December 31, 1997 (File No. 0-13299).
10.03	Management Agreement among the Partnership, Demeter and
Graham Capital Management, L.P. dated as of January 1,
2003, is incorporated by reference to Exhibit 10.01 of
the Partnership's Form 8-K (File No. 0-13299) filed with
the Securities and Exchange Commission on January 22,
2003.
10.04	Dean Witter Cornerstone Funds Exchange Agreement, dated
as of May 31, 1984, is incorporated by reference to
Exhibit 10.06 of the Partnership's Annual Report on Form
10-K for the fiscal year ended September 30, 1984 (File
No. 0-13299).
10.05	Amended and Restated Customer Agreement between the
Partnership and Morgan Stanley DW Inc., dated as of June
22, 2000, is incorporated by reference to Exhibit 10.01
of the Partnership's Form 8-K (File No. 0-13299) filed
with the Securities and Exchange Commission on November
13, 2001.
<page>
10.06	Commodity Futures Customer Agreement between Morgan
Stanley & Co. Incorporated and the Partnership, and
acknowledged and agreed to by Morgan Stanley DW Inc.,
dated as of May 1, 2000, is incorporated by reference to
Exhibit 10.02 of the Partnership's Form 8-K (File No. 0-
13299) filed with the Securities and Exchange Commission
on November 13, 2001.
10.07	Customer Agreement between the Partnership and Morgan
Stanley & Co. International Limited, dated as of May 1,
2000, is incorporated by reference to Exhibit 10.04 of
the Partnership's Form 8-K (File No. 0-13299) filed with
the Securities and Exchange Commission on November 13,
2001.
10.08	Foreign Exchange and Options Master Agreement between
Morgan Stanley & Co. Incorporated and the Partnership,
dated as of April 30, 2000, is incorporated by reference
to Exhibit 10.05 of the Partnership's Form 8-K (File
No. 0-13299) filed with the Securities and Exchange
Commission on November 13, 2001.
10.09	Amendment to Management Agreement between the Partnership
and Welton Investment Corporation, dated as of November
30, 2000, is incorporated by reference to Exhibit 10.1 of
the Partnership's Form 8-K (File No. 0-13299) filed with
the Securities and Exchange Commission on January 3,
2001.
10.10	Amendment to Management Agreement between the Partnership
and Sunrise Capital Management, Inc., dated as of
November 30, 2000, is incorporated by reference to the
Partnership's Form 8-K (File No. 0-13299) filed with the
Securities and Exchange Commission on January 3, 2001.
10.11	Securities Account Control Agreement among the
Partnership, Morgan Stanley & Co. Incorporated, and
Morgan Stanley DW Inc., dated as of May 1, 2000, is
incorporated by reference to Exhibit 10.03 of the
Partnership's Form 8-K (File No. 0-13299) filed with the
Securities and Exchange Commission on November 13, 2001.
31.01	Certification of President of Demeter Management
Corporation, the general partner of the Partnership,
pursuant to rules 13a-15(e) and 15d-15(e), as adopted
pursuant to Section 302 of the Sarbanes-Oxley Act of
2002.

<page>
31.02	Certification of Chief Financial Officer of Demeter
Management Corporation, the general partner of the
Partnership, pursuant to rules 13a-15(e) and 15d-15(e),
as adopted pursuant to Section 302 of the Sarbanes-Oxley
Act of 2002.
32.01	Certification of President of Demeter Management
Corporation, the general partner of the Partnership,
pursuant to 18 U.S.C. Section 1350, as adopted pursuant
to Section 906 of the Sarbanes-Oxley Act of 2002.
32.02	Certification of Chief Financial Officer of Demeter
Management Corporation, the general partner of the
Partnership, pursuant to 18 U.S.C. Section 1350, as
adopted pursuant to Section 906 of the Sarbanes-Oxley Act
of 2002.

(B)	  Reports on Form 8-K
On April 14, 2004 the Partnership filed the Current Report on Form
8-K for the purpose of reporting, under Item 5, changes made to
the Board of Directors of Demeter.








<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 17, 2004         By:   /s/Jeffrey D. Hahn
                              Jeffrey D. Hahn
                              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.