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                                                                   EXHIBIT 10.13


                      THIRD AMENDMENT TO RIGHTS AGREEMENT

         This Third Amendment (the "Amendment") is made effective as of the 21
day of August, 2001, by and between Exabyte Corporation, a Delaware corporation
(the "Company"), and Fleet National Bank (f/k/a the First National Bank of
Boston, the "Bank of Boston"), as Rights Agent, as that term is defined in that
certain Rights Agreement dated as of January 24, 1991, as amended by that
certain First Amendment to Rights Agreement (the "First Amendment") dated as of
August 23, 1995 and that certain Second Amendment to Rights Agreement (the
"Second Amendment") dated as of February 1, 2001 (as so amended, the "Rights
Agreement").

         WHEREAS, holders of the Common Shares (as defined in the Rights
Agreement) of the Company were granted certain stock purchase rights (the
"Rights") subject to the conditions set forth in the Rights Agreement;

         WHEREAS, the Company believes that amending the Rights Agreement to
permit a proposed merger between the Company and Ecrix Corporation is desirable
and also wishes to maintain in place the Rights Agreement for the protection of
the stockholder value of the Company as contained in the Rights Agreement;

         WHEREAS, the Company believes that the merger is in the best interests
of the Company and its stockholders;

         WHEREAS, the Board has determined it is necessary to amend and restate
Section 1(a) in order to conform to the amendment contemplated by the foregoing
preambles; and

         WHEREAS, Fleet National Bank (f/k/a as the Bank of Boston), as Rights
Agent has determined that such amendment would not adversely affect its interest
under the Rights Agreement.

         NOW THEREFORE, the parties hereby agree as follows:

                  1. Certain capitalized terms used herein shall have the
respective meanings given them in the Rights Agreement.

                  2. Section 1(a) of the Rights Agreement is hereby amended and
restated to read in full as follows:

                  (a) "Acquiring Person" shall mean any Person (as such term is
hereinafter defined) who or which, together with all Affiliates and Associates
(as such terms are hereinafter defined) of such Person, shall be the Beneficial
Owner (as such term is hereinafter defined) of 20% or more of the Common Shares
of the Company then outstanding, but shall not include the Company, any
Subsidiary (as such term is hereinafter defined) of the Company, any employee
benefit plan of the Company or any Subsidiary of the Company, or any entity
holding Common Shares for or pursuant to the terms of any such plan.


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         The definition of "Acquiring Person" shall not include:

                           i) the persons listed on Exhibit D to this Rights
                  Agreement (the "Investors"); or

                           ii) the Affiliates or Associates of such Investors;

unless and until such time as: (a) all of such Investors together with all such
Investors' Affiliates and Associates beneficially own the greater of (1) more
than 20,000,000 Common Shares or (2) more than 49.999% of the Common Shares then
outstanding, in which event all such Investors shall immediately become
Acquiring Persons; (b) Meritage Private Equity Fund, L.P. ("Meritage") and its
Affiliates and Associates, beneficially own 25% or more of the Common Shares
then outstanding (disregarding for this purpose Common Shares beneficially owned
by other Investors), in which event Meritage and its Affiliates and Associates
shall immediately become Acquiring Persons; or (c) any Investor other than
Meritage (an "Other Investor"), together with such Other Investor's Affiliates
and Associates, beneficially own 20% or more of the Common Shares then
outstanding (disregarding for this purpose Common Shares beneficially owned by
Meritage and any other Investors), in which event such Other Investor and its
Affiliates and Associates shall immediately become Acquiring Persons.

         No Person that owns Common Shares and acquires control of an Investor
shall become an Acquiring Person, and no Investor that acquires control of
another Person who owns Common Shares shall become an Acquiring Person (even if
the combined ownership of the Persons and Investors that are parties to such
acquisition, and their Affiliates and Associates, exceeds 20% (or if Meritage is
involved in such acquisition, either as the acquired or the acquiring party,
even if the combined ownership exceeds 25%)), provided that the affected
Investor or other Person, as the case may be, as promptly as practicable after
such acquisition takes such actions to reduce the number of Common Shares such
Investor or other Person, as the case may be, together with all its Affiliates
and Associates, is the beneficial owner of to less than 20% (or if Meritage is
involved in such acquisition, either as the acquired or acquiring party, then
such beneficial ownership reduction shall be to less than 25%).

         Notwithstanding the foregoing, no Person shall become an "Acquiring
Person" as the result of an acquisition of Common Shares by the Company which,
by reducing the number of shares outstanding, increases the proportionate number
of shares beneficially owned by such Person to 20% or more of the Common Shares
of the Company then outstanding; provided, however, that if a Person shall
become the Beneficial Owner of 20% or more of the Common Shares of the Company
then outstanding by reason of share purchases by the Company and shall, after
such share purchases by the Company, become the Beneficial Owner of any
additional Common Shares of the Company, then such Person shall be deemed to be
an "Acquiring Person." Notwithstanding the foregoing, if the Board of Directors
of the Company determines in good faith that a Person who would otherwise be an
"Acquiring Person," as defined pursuant to the foregoing provisions of this
Section 1(a) has become such inadvertently, and such Person divests as promptly
as practicable a sufficient number of Common Shares so that


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such Person would no longer be an Acquiring Person, as defined pursuant to the
foregoing provisions of this Section 1(a), then such Person shall not be deemed
to be an "Acquiring Person" for any purposes of this Agreement.

                  3. Except as expressly provided by this Amendment, all other
terms and conditions of the Rights Agreement shall remain in full force and
effect.

                  4. This Amendment may be executed in two counterparts, and
each of such counterparts shall for all purposes be deemed to be an original,
and both of such counterparts shall together constitute but one and the same
instrument.

         IN WITNESS WHEREOF, the Company and the Fleet National Bank (f/k/a Bank
of Boston) have executed this Amendment as of the date first above written.


EXABYTE CORPORATION                    FLEET NATIONAL BANK
                                       (f/k/a The First National Bank of Boston)


By:    /s/ William L. Marriner         By:    /s/ Tyler Haynes
       -----------------------                ----------------------------------
Name:  William L. Marriner             Name:  Tyler Haynes
Title: President                       Title: Managing Director




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                                    EXHIBIT D

                                    INVESTORS

<Table>
<S>                                                            <C>
Meritage Private Equity Fund, L.P.                             Hexagon Investments LLC

Meritage Private Equity Parallel Fund, L.P.                    Grandhaven LLC

Meritage Entrepreneurs Fund, L.P.                              Legacy Enterprises LLC

Millennial Holdings LLC                                        Labyrinth Enterprises LLC

The Millennial Fund                                            James Monroe III, Grantor Trust

Tankersley Family Limited Partnership                          Valley Ventures II, L.P.

Centennial Fund V, L.P.                                        Curtis R. Jensen

Centennial Entrepreneurs Fund V, L.P.                          William J. Almon, Sr.

Centennial Fund VI, L.P.                                       Mark Rossi

Centennial Entrepreneurs Fund VI, L.P.

Centennial Holdings I, LLC

Big Partners V, L.P.
</Table>