SECOND AMENDMENT TO SUPPLY AGREEMENT

        THIS IS A SECOND AMENDMENT TO SUPPLY AGREEMENT dated as of May 13, 2002
(the "Second  Amendment"),  between  CONE MILLS  CORPORATION,  a North  Carolina
corporation ("Cone"), and LEVI STRAUSS & CO., a Delaware corporation ("LS&CO.").

                               B A C K G R O U N D

        Cone and LS&CO. are  parties to a Supply  Agreement,  dated as of March
30, 1992, as amended by a First Amendment to Supply  Agreement dated as of April
15,  1992  (as  amended,  the  "1992  Agreement").  In  view  of the  increasing
globalization of fabric and apparel product manufacturing,  potential changes in
duty and tariff policies and other developments in their respective  businesses,
they wish to amend the 1992 Agreement to modify the requirements and exclusivity
features of the 1992 Agreement.  This Second  Amendment is intended to be and is
an "instrument in writing signed by both parties" as  contemplated  by Section 9
of the 1992 Agreement.

CONE AND LS&CO. AGREE AS FOLLOWS:


1.      AMENDMENT TO SECTION 1

          1.1 AMENDMENT TO SECTION 1.6.  Section 1.6 of the Agreement is amended
by  replacing  "XXX Denim" with "01 Denim." As a result of this  amendment  to a
defined  term,  all uses in the  Agreement of "XXX Denim" are now changed to "01
Denim."

2.      AMENDMENTS TO SECTION 2

          2.1 AMENDMENT TO HEADING. The heading of Section 2 of the Agreement is
amended by replacing "Requirements Agreement" with "01 Denim Supply".

          2.2 AMENDMENT TO SECTION 2.1.  Section 2.1 of the Agreement is amended
in its entirety as follows:

          (a) Cone agrees to manufacture and sell to LS&CO. all 01 Denim LS&CO.
          may order from Cone.


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          (b) From the date of this Second  Amendment until March 30, 2003, Cone
          shall sell 01 Denim only to LS&CO. After March 30, 2003, Cone may sell
          01 Denim to customers other than LS&CO.

          (c) From the date of this  Second  Amendment  until  March  30,  2003,
          LS&CO.  shall purchase from Cone all 01 Denim that LS&CO.  may require
          in its worldwide businesses. After March 30, 2003, LS&CO. may purchase
          and accept  deliveries of 01 Denim from suppliers other than Cone, and
          use such denim in  501(R)jeans  and other  products for sale in any or
          all of its worldwide businesses.  In addition, if at any time prior to
          March 30, 2003 material additional tariffs,  duties,  imposts or other
          charges are  imposed on the import of 01 Denim from the United  States
          to locations where denim is imported for use in producing  501(R)jeans
          to be sold in LS&CO.'s European, Middle East and Africa region, LS&CO.
          may purchase and accept  deliveries of 01 Denim from  suppliers  other
          than Cone,  and use such denim in  501(R)jeans  and other products for
          sale in that region.

          (d)  Notwithstanding  Sections  2.1(a) and  2.1(c),  and for  clarity,
          LS&CO. may at any time engage in identifying  alternative suppliers in
          all regions of 01 Denim or other denims for 501(R)jeans  ("Alternative
          Suppliers"),   developing  with  and  evaluating  fabrics  from  those
          Alternative  Suppliers,  purchasing and accepting deliveries of fabric
          from Alternative  Suppliers for pre-production and production testing,
          constructing  prototype  and other  jeans of such  fabric  during such
          evaluation  and testing  processes and ultimately  distributing  those
          test products through  whatever means LS&CO. may choose.  In addition,
          LS&CO.  may at any  time  pre-book  capacity  and  place  orders  with
          Alternative   Suppliers;   the  limitations  on  alternative  sourcing
          described  in  Sections  2.1(a) and 2.1(c)  limit only  acceptance  of
          deliveries  from  Alternative   Suppliers  for  commercial  production
          purposes.

          (e) Affiliates and licensees of LS&CO., including, without limitation,
          Levi Strauss & Co.  Europe S.A.,  buy 01 Denim from Cone. In addition,
          Cone may create  subsidiaries or enter into joint ventures,  alliances
          or other  arrangements  through which  entities  other than Cone Mills
          Corporation produce and/or sell 01 Denim. For example, Cone and LS&CO.
          are concurrently  with this Second Amendment  concluding  arrangements
          relating to production of 01 Denim by a party in Europe with whom Cone
          intends to enter into a joint venture.  For clarity,  it is understood
          that,  for purposes of this Section 2, "LS&CO."  means LS&CO.  and its
          affiliates,  and "Cone" means Cone and any subsidiaries or other third
          parties who produce and sell 01 Denim under agreement with Cone.


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3.      REPRESENTATIONS AND WARRANTIES

          3.1 BY LS&CO. LS&CO.  represents and warrants to Cone that: (i) LS&CO.
has full corporate power and authority to enter into and perform its obligations
under  this  Second  Amendment  and the  Agreement;  (ii)  each  of this  Second
Amendment  and the  Agreement as amended by this Second  Amendment has been duly
executed and delivered by LS&CO.  and constitutes  the legal,  valid and binding
obligation of LS&CO.,  enforceable  against it in accordance with its terms; and
(iii) LS&CO. is not a party to, subject to or bound by any agreement,  contract,
lease, mortgage,  indenture or other document of any kind (including any credit,
note purchase,  stock purchase,  receivables purchase,  receivables servicing or
other  financing  agreement) or any law,  judgment,  order,  writ,  prohibition,
injunction or decree of any court or other governmental body that would prevent,
or that would be breached  or  violated  by, or require the consent of any third
party  to,  the  execution  and  delivery  of  this  Second   Amendment  or  the
consummation  of the  transactions  contemplated  by the Agreement as amended by
this Second Amendment.

          3.2 BY CONE. Cone represents and warrants to LS&CO. that: (i) Cone has
full  corporate  power and  authority to enter into and perform its  obligations
under  this  Second  Amendment  and the  Agreement;  (ii)  each  of this  Second
Amendment  and the  Agreement as amended by this Second  Amendment has been duly
executed and  delivered  by Cone and  constitutes  the legal,  valid and binding
obligation  of Cone  enforceable  against it in accordance  with its terms;  and
(iii) Cone is not a party to,  subject to or bound by any  agreement,  contract,
lease, mortgage,  indenture or other document of any kind (including any credit,
note purchase,  stock purchase,  receivables purchase,  receivables servicing or
other  financing  agreement) or any law,  judgment,  order,  writ,  prohibition,
injunction or decree of any court or other governmental body that would prevent,
or that would be breached  or  violated  by, or require the consent of any third
party  to,  the  execution  and  delivery  of  this  Second   Amendment  or  the
consummation  of the  transactions  contemplated  by the Agreement as amended by
this Second Amendment.  Cone acknowledges that nothing in this Agreement commits
LS&CO.  to order or buy from  Cone  any 01 Denim or any  other  product,  in any
quantity  or at any time,  in the  future,  or to continue to produce and market
products containing 01 Denim.

4.      NO OTHER MODIFICATIONS

          Except as  expressly  described  in this  Second  Amendment,  Cone and
LS&CO.  do not  intend  to and are not  modifying  any other  provisions  of the
Agreement,  and the Agreement,  as amended by this Second Amendment,  remains in
full force and effect.

                                     * * * *


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        IN WITNESS  WHEREOF,  the parties  have caused this Second Amendment to
be  executed  by their duly  authorized  officers  as of the date and year first
above written.

                                        CONE MILLS CORPORATION

                                        By: /s/Gary L. Smith
                                            Gary L. Smith
                                            Executive Vice President
                                            and Chief Financial Officer


                                        LEVI STRAUSS & CO.

                                        By: /s/William B. Chiasson
                                            William B. Chiasson
                                            Senior Vice President
                                            and Chief Financial Officer