<PAGE>   1
                                                                     EXHIBIT 4.3

                       FIRST AMENDMENT TO PREFERRED SHARE
                            PURCHASE RIGHTS AGREEMENT


     This First Amendment to Preferred Share Purchase Rights Agreement (this
"Amendment") is made and entered into effective this __ day of September 1998 by
and between Crescent Operating, Inc., a Delaware corporation (the "Company"),
and BankBoston, N.A., as Rights Agent (the "Rights Agent"), with reference to
that certain Preferred Share Purchase Rights Agreement, dated as of June 11,
1997, by and between the Company and the Rights Agent (the "Rights Agreement").
Each capitalized term used in this Amendment and not defined herein shall have
the respective meaning ascribed to such term in the Rights Agreement.


     WHEREAS, the Board of Directors of the Company has approved and adopted
this Amendment and the terms hereof;


     WHEREAS, the Company has authorized certain of its officers and directors
to execute and deliver this Amendment on behalf of the Company;


     NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein set forth, the Company and the Rights Agent hereby agree as follows.


     1. Amendment to Section 1(a). Section 1(a) of the Rights Agreement is
hereby amended by deleting such section in its entirety and substituting for
such section, as a replacement Section 1(a), the following:


     (a) "Acquiring Person" shall mean any Person who or which, together with
     all Affiliates and Associates of such Person, shall be the Beneficial Owner
     of 10% or more of the Common Shares of the Company then outstanding but
     shall not include (i) the Company, (ii) any Subsidiary of the Company,
     (iii) any employee benefit plan of the Company or of any Subsidiary of the
     Company, or any entity holding Common Shares for or pursuant to the terms
     of any such plan, (iv) Crescent and its controlled Affiliates and its
     directors and executive officers and their controlled Affiliates, or (v)
     Gotham Partners, L.P., together with all Affiliates and Associates thereof
     (collectively, "Gotham"), but only if and to the extent that Gotham,
     together with all Affiliates and Associates thereof, shall be the
     Beneficial Owner of 15% or less of the Common Shares of the Company then
     outstanding. Notwithstanding anything in this definition of Acquiring
     Person to the contrary, no Person shall become an "Acquiring Person" as the
     result of an 

<PAGE>   2


        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 10% or more of the Common
        Shares of the Company then outstanding (or, in the case of Gotham, to
        more than 15% of the Common Shares of the Company then outstanding);
        provided, however, that if a Person shall become the Beneficial Owner of
        10% or more of the Common Shares of the Company then outstanding, or if
        Gotham shall become the Beneficial Owner of more than 15% 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 anything in this definition of Acquiring Person to the
        contrary, if the Board of Directors determines in good faith that a
        Person who would otherwise be an "Acquiring Person," as defined pursuant
        to the foregoing provisions of this paragraph (a), has become such
        inadvertently, and such Person divests as promptly as practicable a
        sufficient number of Common Shares so that such Person would no longer
        be an "Acquiring Person," as defined pursuant to the foregoing
        provisions of this paragraph (a), then such Person shall not be deemed
        to be an "Acquiring Person" for any purposes of this Agreement.

        2. Amendment to Section 3(a). Section 3(a) of the Rights Agreement is
hereby amended by deleting such section in its entirety and substituting for
such section, as a replacement Section 3(a), the following:


        (a) Until the earlier of (i) the tenth day after the Shares Acquisition
        Date or (ii) the tenth Business Day (or such later date as may be
        determined by action of the Board of Directors prior to such time as any
        Person becomes an Acquiring Person) after the date of the commencement
        by any Person (other than the Company, any Subsidiary of the Company,
        any employee benefit plan of the Company or of any Subsidiary of the
        Company, any entity holding Common Shares for or pursuant to the terms
        of any such plan, or, any Crescent Affiliate) of, or of the first public
        announcement of the intention of any Person (other than the Company, any
        Subsidiary of the Company, any employee benefit plan of the Company or
        of any Subsidiary of the Company, any entity holding Common Shares for
        or pursuant to the terms of any such plan or, any Crescent Affiliate) to
        commence, a tender or exchange offer the consummation of which would
        result in any Person becoming an 

                                       2
<PAGE>   3


        Acquiring Person (the earlier of such dates being herein referred to as
        the "Rights Distribution Date"), (x) the Rights will be evidenced
        (subject to the provisions of Section 3(b) hereof) by the certificates
        for Common Shares registered in the names of the holders thereof (which
        certificates shall also be deemed to be Right Certificates) and not by
        separate Right Certificates, and (y) the right to receive Right
        Certificates will be transferable only in connection with the transfer
        of Common Shares. As soon as practicable after the Rights Distribution
        Date, the Company will prepare and execute, the Rights Agent will
        countersign, and the Company will send or cause to be sent (and the
        Rights Agent will, if requested, send) by first-class, postage-prepaid
        mail, to each record holder of Common Shares as of the Close of Business
        on the Rights Distribution Date, at the address of such holder shown on
        the records of the Company, a Right Certificate, in substantially the
        form of Exhibit B hereto (a "Right Certificate"), evidencing one Right
        for each Common Share so held. From and after the Rights Distribution
        Date, the Rights will be evidenced solely by such Right Certificates.

        3. Amendment to Exhibit C. Exhibit C to the Rights Plan is hereby
amended by deleting such exhibit in its entirety and substituting for such
exhibit, as a replacement, the attached Exhibit C-1.


        4. Effect on Rights Plan. On and after the date of this Amendment, each
reference in the Rights Plan to "this Agreement," "hereunder," "hereof,"
"herein" or words of like import referring to the Rights Plan shall mean and be
a reference to the Rights Plan as amended by this Amendment, and this Amendment
shall be deemed to be a part of the Rights Plan. Except as specifically amended
by this Amendment, (i) the Rights Plan is hereby ratified and confirmed, and
(ii) the terms and provisions of the Rights Plan shall remain in full force and
effect.

        5. Applicable Law. This Amendment shall be governed by and construed in
accordance with the laws of the State of Delaware applicable to contracts made
and to be performed entirely within such State.


                                       3

<PAGE>   4




     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered by their respective officers thereunto duly
authorized as of the date written above.



                                            CRESCENT OPERATING, INC.


                                            By:
                                               ----------------------------
                                               Its
                                                  -------------------------



                                            BANKBOSTON, N.A.


                                            By:
                                               ----------------------------
                                               Its
                                                  -------------------------

                                       4

<PAGE>   5



                                   Exhibit C-1


                                     Form of


                          SUMMARY OF RIGHT TO PURCHASE


                                PREFERRED SHARES


     On June 12, 1997, the Board of Directors of Crescent Operating, Inc. (the
"Company") declared a dividend of one preferred share purchase right (a "Right")
for each outstanding share of common stock, par value $.01 per share, of the
Company (the "Common Shares"). The dividend was payable on June 12, 1997 to the
stockholders of record on that date (the "Record Date"). Each Right entitles the
registered holder to purchase from the Company one one-hundredth of a share of
Series A Junior Participating Preferred Stock, par value $.01 per share, of the
Company (the "Preferred Shares") at a price of $5 per one one-hundredth of a
Preferred Share (the "Purchase Price"), subject to adjustment. The description
and terms of the Rights are set forth in a Rights Agreement (the "Rights
Agreement") between the Company and BankBoston, N.A., as Rights Agent (the
"Rights Agent"). Until the earlier to occur of (i) 10 days following a public
announcement that a person or group of affiliated or associated persons has
acquired beneficial ownership of 10% or more of the outstanding Common Shares
(subject to certain exceptions described generally below, an "Acquiring Person")
or (ii) 10 business days (or such later date as may be determined by action of
the Board of Directors of the Company prior to such time as any person or group
of affiliated persons becomes an Acquiring Person) following the commencement
of, or announcement of an intention to make, a tender offer or exchange offer
the consummation of which would result in any person or group of affiliated
persons becoming an Acquiring Person (the earlier of such dates being the
"Rights Distribution Date"), the Rights will be evidenced, with respect to any
of the Common Share certificates Outstanding as of the Record Date, by such
Common Share certificate with a copy of this Summary of Rights attached thereto.
The Rights Agreement contains exceptions from its operating provisions for (i)
Crescent and certain of its affiliates and (ii) Gotham Partners, L.P., together
with its affiliates and associates, but only if and to the extent that Gotham
Partners, L.P., together with its affiliates and associates, have beneficial
ownership of 15% or less of the outstanding Common Shares.

                                       C-1
<PAGE>   6

     The Rights Agreement provides that, until the Rights Distribution Date (or
earlier redemption or expiration of the Rights), the Rights will be transferred
with and only with the Common Shares. Until the Rights Distribution Date (or
earlier redemption or expiration of the Rights), new Common Share certificates
issued after the Record Date upon transfer or new issuance of Common Shares will
contain a notation incorporating the Rights Agreement by reference. Until the
Rights Distribution Date (or earlier redemption or expiration of the Rights),
the surrender for transfer of any certificates for Common Shares outstanding as
of the Record Date, even without such notation or a copy of this Summary of
Rights being attached thereto, will also constitute the transfer of the Rights
associated with the Common Shares represented by such certificates. As soon as
practicable following the Rights Distribution Date, separate certificates
evidencing the Rights ("Right Certificates") will be mailed to holders of record
of the Common Shares as of the close of business on the Rights Distribution Date
and such separate Right Certificates alone will evidence the Rights.

     The Rights are not exercisable until the Rights Distribution Date. The
Rights will expire on the date which is the tenth anniversary of the Record Date
(the "Final Expiration Date"), unless the Final Expiration Date is extended or
unless the Rights are earlier redeemed or exchanged by the Company, in each
case, as described below.

     The Purchase Price payable, and the number of Preferred Shares or other
securities or property issuable, upon exercise of the Rights are subject to
adjustment from time to time to prevent dilution (i) in the event of a stock
dividend on, or a subdivision, combination or reclassification of, the Preferred
Shares; (ii) upon the grant to holders of the Preferred Shares of certain rights
or warrants to subscribe for or purchase Preferred Shares at a price, or
securities convertible into Preferred Shares with a conversion price, less than
the then-current market price of the Preferred Shares; or (iii) upon the
distribution to holders of the Preferred Shares of evidences of indebtedness or
assets (excluding regular periodic cash dividends paid out of earnings or
retained earnings or dividends payable in Preferred Shares) or of subscription
rights or warrants (other than those referred to above).

     The number of outstanding Rights and the number of one one-hundredths of a
Preferred Share issuable upon exercise of each Right are also subject to
adjustment in the event of a stock split of the Common Shares or a stock
dividend on the Common Shares payable in Common Shares or subdivisions,
consolidations or combinations of the Common Shares occurring, in any such case,
prior to the Rights Distribution Date.

                                      C-2
<PAGE>   7

     Preferred Shares purchasable upon exercise of the Rights will not be
redeemable. Each Preferred Share will be entitled to a minimum preferential
quarterly dividend payment of $1 per share but will be entitled to an aggregate
dividend of 100 times the dividend declared per Common Share. In the event of
liquidation, the holders of the Preferred Shares will be entitled to a minimum
preferential liquidation payment of $100 per share but will be entitled to an
aggregate payment of 100 times the payment made per Common Share. Each Preferred
Share will have 100 votes, voting together with the Common Shares. Finally, in
the event of any merger, consolidation or other transaction in which Common
Shares are exchanged, each Preferred Share will be entitled to receive 100 times
the amount received per Common Share. These rights are protected by customary
antidilution provisions.

     Because of the nature of the Preferred Shares' dividend, liquidation and
voting rights, the value of the one one-hundredth interest in a Preferred Share
purchasable upon exercise of each Right should approximate the value of one
Common Share.

     In the event that the Company is acquired in a merger or other business
combination transaction or 50% or more of its consolidated assets or earning
power are sold after a person or group has become an Acquiring Person, proper
provision will be made so that each holder of a Right will thereafter have the
right to receive, upon the exercise thereof at the then current exercise price
of the Right, that number of shares of common stock of the acquiring company
which at the time of such transaction will have a market value of two times the
exercise price of the Right. In the event that any person or group of affiliated
or associated persons becomes an Acquiring Person, proper provision shall be
made so that each holder of a Right, other than Rights beneficially owned by the
Acquiring Person (which will thereafter be void), will thereafter have the right
to receive upon exercise that number of Common Shares having a market value of
two times the exercise price of the Right.

     At any time after any person or group becomes an Acquiring Person and prior
to the acquisition by such person or group of 50% or more of the outstanding
Common Shares, the Board of Directors of the Company may exchange the Rights
(other than Rights owned by such person or group which will have become void),
in whole or in part, at an exchange ratio of one Common Share, or one
one-hundredth of a Preferred Share, per Right (subject to adjustment).

     With certain exceptions, no adjustment in the Purchase Price will be
required until cumulative adjustments require an adjustment of at least 1% in
such Purchase Price.

                                      C-3
<PAGE>   8

     No fractional Preferred Shares will be issued (other than fractions which
are integral multiples of one one-hundredth of a Preferred Share, which may, at
the election of the Company, be evidenced by depositary receipts) and, in lieu
thereof, an adjustment in cash will be made based on the market price of the
Preferred Shares on the last trading day prior to the date of exercise.

     At any time prior to the time that any person or group of affiliated or
associated persons becomes an Acquiring Person, the Board of Directors of the
Company may redeem the Rights in whole, but not in part, at a price of $.01 per
Right (the "Redemption Price"). The redemption of the Rights may be made
effective at such time on such basis with such conditions as the Board of
Directors in its sole discretion may establish. Immediately upon any redemption
of the Rights, the right to exercise the Rights will terminate and the only
right of the holders of Rights will be to receive the Redemption Price.

     The terms of the Rights may be amended by the Board of Directors of the
Company without the consent of the holders of the Rights, except that from and
after such time as any person or group of affiliated or associated persons
becomes an Acquiring Person no such amendment may adversely affect the interests
of the holders of the Rights.

     Until a Right is exercised, the holder thereof, as such, will have no
rights as a stockholder of the Company, including, without limitations the right
to vote or to receive dividends.

     A copy of the Rights Agreement has been filed with the Securities and
Exchange Commission as an Exhibit to the Company's Quarterly Report on Form 10-Q
for the quarter ended June 30, 1997 (File No. 0-22725). A copy of the Rights
Agreement is available free of charge from the Company. This summary description
of the Rights does not purport to be complete and is qualified in its entirety
by reference to the Rights Agreement, which is hereby incorporated herein by
reference.


                                      C-4