<PAGE>   1

                                                                     EXHIBIT 4.4



                       SECOND AMENDMENT TO PREFERRED SHARE
                            PURCHASE RIGHTS AGREEMENT



         This Second Amendment to Preferred Share Purchase Rights Agreement
(this "Amendment") is made and entered into effective this 4th day of March 1999
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, as previously amended
(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 Company is the sole general partner of and owns a 50%
partnership interest in COPI Colorado, L.P., a Delaware limited partnership
("COPI Colorado");

         WHEREAS, the Company believes that COPI Colorado is or should be
treated as a Subsidiary of the Company;

         WHEREAS, the Board of Directors of the Company has approved and adopted
this Amendment and the terms hereof for the purpose of clarifying that, for so
long as certain conditions are met, COPI Colorado shall be characterized as a
Subsidiary of the Company for purposes of the Rights Agreement;

         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 agree as follows.

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

              (aa) "Subsidiary" of any Person shall mean any corporation or
              other entity of which a majority of the voting power of the voting
              equity securities or equity interest is owned, directly or
              indirectly, by such Person. "Subsidiary," when used with reference
              to the Company, also shall include COPI Colorado as long as (i)
              the Company is the sole general partner of COPI Colorado and (ii)
              the Company owns more than 20% of the aggregate partnership
              interests in COPI Colorado.

         2.   Addition of New Section 1(dd). A new Section 1(dd) is hereby added
to the Rights Agreement, which Section 1(dd) shall read as follows:

              (dd) "Crescent" shall mean Crescent Real Estate Equities Company,
              a Texas real estate investment trust.






<PAGE>   2

         3.   Amendment to Exhibit C-1. Exhibit C-1 is hereby amended by
deleting such exhibit in its entirety and substituting for such exhibit, as a
replacement, the attached Exhibit C-1, dated March 1999.

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

         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 Executive Vice President & 
                                                     ---------------------------
                                                     Chief Operating Officer
                                                     ---------------------------



                                              BANKBOSTON, N.A.

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


                                      -2-

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                                   EXHIBIT C-1
                                  (MARCH 1999)



                                     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 (as amended, 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) the Company, (ii) any subsidiary of the Company,
including (as long as certain conditions are met), COPI Colorado, L.P., (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 Real Estate Equities Company and its controlled affiliates and its
directors and executive officers and their controlled affiliates, and (v) 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. In addition, the Rights Agreement provides that if a person has become
an Acquiring Person inadvertently, and such person divests as promptly as
practicable a sufficient number of Common Shares so as to no longer be an
Acquiring Person, then such person will not be deemed to be an Acquiring Person
for purposes of the Rights Agreement.

         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 




                                     C-1-1

<PAGE>   4


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.

         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).



                                     C-1-2

<PAGE>   5


         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.

         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). In addition, a copy of
the First Amendment to 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 September 30, 1998. A copy of the Second Amendment to
the Rights Agreement will be filed with the Securities and Exchange Commission
as an Exhibit to the Company's Annual Report on Form 10-K for the year ended
December 31, 1998. 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-1-3