<PAGE>
 
                                                                    Exhibit 4.1B
                                                                    ------------
                                                                                
                         Amendment to Rights Agreement
                       dated as of August 5, 1997 between
                         Barrett Resources Corporation
                              and BankBoston, N.A.


     The Rights Agreement is hereby amended as follows:

     1.   The first sentence of the Rights Agreement is amended by adding after
          the words "BankBoston, N.A." and before the parenthetical the
          following:

               , a national banking association

     2.   Section 1 is amended to delete paragraphs (l) and (m) therefrom.

     3.   Section 3(a) is amended by eliminating the first sentence thereof and
          substituting in its place the following:

          Until the earlier of (i) the Stock Acquisition Date or (ii) the tenth
          Business Day after the date of the commencement of, or first public
          announcement of the intent of any Person (other than the Company, any
          subsidiary of the Company, or any employee benefit plan of the Company
          or any of its subsidiaries or any trustee or administrator of any such
          plan in its capacity as such) to commence (which intention to commence
          remains in effect for five business days after such announcement), a
          tender or exchange offer which would result in such Person becoming an
          Acquiring Person (or such later date determined by the Board of
          Directors of the Company which date shall not be later than the date
          specified in (i)), (the earlier of such dates being herein referred to
          as the "Distribution Date"), (x) the Rights will be evidenced (subject
          to the provisions of paragraph (b) of this Section 3) by the
          certificates for Common Stock registered in the names of the holders
          of the Common Stock (which certificates for Common Stock shall be
          deemed also to be certificates for Rights) and not by separate
          certificates, and (y) the Rights (and the right to receive
          certificates therefor) will be transferable only in connection with
          the transfer of the underlying shares of Common Stock (including a
          transfer to the Company); provided, however, that if a tender or
          exchange offer is terminated prior to the occurrence of the
          Distribution Date, then no Distribution Date shall occur as a result
          of that tender or exchange offer.


     4.   Section 4(b) is amended by deleting the two references to "a
          Transaction Person" from the legend.

     5.   Section 7(e) is amended by eliminating the existing text thereof and
          substituting in its place the following:

          Notwithstanding anything in this Agreement to the contrary, from and
          after the time an Acquiring Person first becomes such, any Rights
          beneficially owned by (i) an Acquiring Person or an Affiliate or
          Associate of an 
<PAGE>
 
          Acquiring Person, (ii) a transferee of an Acquiring Person (or of any
          Affiliate or Associate thereof) who becomes a transferee after the
          Acquiring Person becomes such, or (iii) a transferee of an Acquiring
          Person (or of any Affiliate or Associate thereof) who becomes a
          transferee prior to or concurrently with the Acquiring Person becoming
          such and receives such Rights pursuant to either (A) a transfer
          (whether or not for consideration) from the Acquiring Person to
          holders of equity interests in such Acquiring Person or to any Person
          with whom the Acquiring Person has a continuing agreement, arrangement
          or understanding regarding the transferred Rights or (B) a transfer
          which the Board of Directors of the Corporation has determined is part
          of a plan, arrangement or understanding which has as a primary purpose
          or effect the avoidance of this Section 7(e), shall become null and
          void without any further action and no holder of such Rights shall
          have any rights whatsoever with respect to such Rights, whether under
          any provision of this Agreement or otherwise. The Corporation shall
          use all reasonable efforts to insure that the provisions of this
          Section 7(e) and Section 4(b) hereof are complied with, but shall have
          no liability to any holder of Right Certificates or other Person as a
          result of its failure to make any determinations with respect to an
          Acquiring Person or its Affiliates, Associates or transferees
          hereunder.

     6.   Section 13(a) is amended by replacing the language before clause (x)
          with the following:

          In the event that, on or following the Stock Acquisition Date,
          directly or indirectly,

     7.   Section 13 is further amended by deleting Section 13(d).

     8.   Section 24(a)(ii) is amended by deleting the reference to "a
          Transaction Person" therein.

     9.   Section 24(a) is further amended by deleting subsection (iii) thereof.


     10.  Section 26 is amended by changing the address for notices to
          BankBoston, N.A. to the following:

               c/o Equiserve Limited Partnership
               150 Royall Street
               Canton, MA 02021
               Attention:  Client Administration

     11.  Section 27 is amended by deleting the last sentence of the Section.

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     12.  Exhibit C to the Rights Agreement is amended by replacing the attached
          "Exhibit C" in its place.

                         BARRETT RESOURCES CORPORATION


                         By: /s/ A. Ralph Reed
                             ---------------------------------
                             A. Ralph Reed
                             President and Chief Operating Officer

                         BANKBOSTON, N.A.


                         By: /s/ Carol Mulvey-Eori
                             ---------------------------------
                             Name:  Carol Mulvey-Eori
                             Title:    _______________________

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<PAGE>
 
                                                                       Exhibit C
                                                                       ---------

                         SUMMARY OF RIGHTS TO PURCHASE

                                PREFERRED STOCK

          On August 4, 1997, the Board of Directors of Barrett Resources
Corporation (the "Company") declared a dividend distribution of one Right for
each outstanding share of common stock, par value $.001 per share (the "Common
Stock"), of the Company to stockholders of record at the close of business on
August 20, 1997 (the "Record Date").  Except as set forth below, each Right,
when exercisable, entitles the registered holder to purchase from the Company
one one-thousandth of a share of a series of preferred stock, designated as
Series A Junior Participating Preferred Stock, par value $.01 per share (the
"Preferred Stock"), at a price of $150 per one one-thousandth of a 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, and an amendment to the Rights
Agreement dated as of February 25, 1999 (the "Amendment").

          Until the earlier to occur of (i) a public announcement that, without
the prior consent of the Board of Directors of the Company, a person or group of
affiliated or associated persons (an "Acquiring Person") has acquired, or
obtained the right to acquire, beneficial ownership of 15% or more of the
outstanding shares of Common Stock (the "Stock Acquisition Date"), or (ii) ten
business days (or such later date as the Board may determine) following the
commencement of (or a public announcement of an intention to make) a tender
offer or exchange offer which would result in any person or group and related
persons having beneficial ownership of 15% or more of the outstanding shares of
Common Stock without the prior consent of the Board of Directors of the Company
(the earlier of such dates being called the "Distribution Date"), the Rights
will be evidenced, with respect to any of the Common Stock certificates
outstanding as of August 20, 1997, by such Common Stock certificate and no
separate Rights Certificates will be distributed.  The Rights Agreement, as
amended, provides that, until the Distribution Date, the Rights will be
transferred with and only with Common Stock certificates.  Until the
Distribution Date (or earlier redemption or expiration of the Rights), new
Common Stock certificates issued after August 20, 1997, (or as soon thereafter
as practicable) upon transfer or new issuance of the Common Stock will contain a
notation incorporating the Rights Agreement, as amended, by reference.  Until
the Distribution Date (or earlier redemption or expiration of the Rights), the
surrender for transfer of any certificates for Common Stock outstanding as of
August 20, 1997, will also constitute the transfer of the Rights associated with
the Common Stock represented by such certificate, even without such notation.
As soon as practicable following the Distribution Date, separate certificates
evidencing the Rights ("Rights Certificates") will be mailed to holders of
record of the Common Stock as of the close of business on the Distribution Date,
and the separate Rights Certificates alone will evidence the Rights.

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<PAGE>
 
          The Rights are not exercisable until the Distribution Date.  The
Rights will expire on August 4, 2007, unless earlier redeemed by the Company as
described below.

          In the event that any person becomes an Acquiring Person, each holder
of a Right generally will thereafter have the right for a 60 day period after
the later of the date of such event or the effectiveness of an appropriate
registration statement (or such other longer period set by the Board of
Directors) to receive upon exercise of the Right that number of units of one
one-thousandths of a share of Preferred Stock (or, under certain circumstances,
Common Stock or other securities) having an average market value during a
specified time period (immediately prior to the occurrence of a Person becoming
an Acquiring Person) of two times the exercise price of the Right (such right
being called the "Subscription Right").  Notwithstanding the foregoing,
following the occurrence of a Person becoming an Acquiring Person, all Rights
that are, or (under certain circumstances specified in the Rights Agreement)
were, beneficially owned by the Acquiring Person or any affiliate or associate
thereof will be null and void.

          In the event that, at any time following the Stock Acquisition Date,
the Company is acquired in a merger or other business combination transaction or
50% or more of the Company's assets or earning power are sold (in one
transaction or a series of transactions), proper provision shall be made so that
each holder of a Right (except a Right voided as set forth above) shall
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 (or, in the event there is more than one acquiring
company, the acquiring company receiving the greatest portion of the assets or
earning power transferred) which at the time of such transaction would have a
market value of two times the exercise price of the Right (such right being
called the "Merger Right").  The holder of a Right will continue to have the
Merger Right whether or not such holder exercises the Subscription Right.

          The Purchase Price payable, the number of Rights and the number of
units of one one-thousandths of a share of Preferred Stock or shares of the
Common Stock 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 Stock, (ii) upon the grant to holders of the
Preferred Stock of certain rights or warrants to subscribe for Preferred Stock,
certain convertible securities or securities having the same or more favorable
rights, privileges and preferences as the Preferred Stock at less than the
current market price of the Preferred Stock or (iii) upon the distribution to
holders of the Preferred Stock of evidences of indebtedness or assets (excluding
regular quarterly cash dividends out of earnings or retained earnings and
dividends payable in Preferred Stock) or of subscription rights or warrants
(other than those referred to above).

          With certain exceptions, no adjustments in the Purchase Price will be
required until cumulative adjustments require an adjustment of at least 1% in
such Purchase Price.  No fractions of shares will be issued and, in lieu
thereof, an adjustment

                                       5
<PAGE>
 
in cash will be made based on the market price of the Common Stock on the last
trading date prior to the date of exercise.

          The number of outstanding Rights associated with each share of Common
Stock and the voting and economic rights of each one one-thousandths of a share
of Preferred Stock issuable upon exercise of each Right are also subject to
adjustment in the event of a stock split of the Common Stock or a stock dividend
on the Common Stock payable in Common Stock or subdivisions, consolidations or
combinations of the Common Stock occurring, in any such case, prior to the
Distribution Date.

          At any time prior to the earlier to occur of (i) the close of business
on the Stock Acquisition Date or (ii) the expiration of the Rights, the Company
may redeem the Rights in whole, but not in part, at a price of $.001 per Right
(the "Redemption Price"), which redemption shall be effective upon the action of
the Board of Directors.  Additionally, following the Stock Acquisition Date and
the expiration of the period during which the Subscription Right is exercisable,
the Board of Directors may redeem the then outstanding Rights in whole, but not
in part, at the Redemption Price provided that such redemption is in connection
with a merger or other business combination transaction or series of
transactions involving the Company in which all holders of Common Stock are
treated alike but not involving an Acquiring Person (or any person who was an
Acquiring Person) or it affiliates or associates.  Upon the effective date of
the 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 Preferred Stock purchasable upon exercise of the Rights will be
nonredeemable and junior to any other series of preferred stock the Company may
issue (unless otherwise provided in the terms of such stock).  Each share of
Preferred Stock will have a preferential quarterly dividend in an amount equal
to the greater of $10.00 and 1,000 times the dividend declared on each Common
Share.  In the event of liquidation, the holders of Preferred Stock will receive
a preferred liquidation payment equal to the greater of $5,000 and 1,000 times
the payment made per Common Share.  Each share of Preferred Stock will have one
vote, voting together with the Common Shares.  In the event of any merger,
consolidation or other transaction in which Common Shares are exchanged, each
share of Preferred Stock will be entitled to receive 1,000 times the amount and
type of consideration received per Common Share.  The rights of the Preferred
Stock as to dividends, liquidation and voting, and in the event of mergers and
consolidations, are protected by customary anti-dilution provisions.  Fractional
shares of Preferred Stock in integral multiples of one one-thousandth of a share
of Preferred Stock will be issuable; however, the Company may elect to
distribute depositary receipts in lieu of such fractional shares.  In lieu of
fractional shares other than fractions that are multiples of one one-thousandth
of a share, an adjustment in cash will be made based on the market price of the
Preferred Stock on the last trading date prior to the date of exercise.

                                       6
<PAGE>
 
          Until a Right is exercised, the holder thereof, as such, will have no
rights as a stockholder of the Company, including, without limitation, the right
to vote or to receive dividends.

          Except as set forth above, the terms of the Rights may be amended by
the Board of Directors of the Company, (i) prior to the Distribution Date in any
manner, and (ii) on or after the Distribution Date to cure any ambiguity, to
correct or supplement any provision of the Rights Agreement which may be
defective or inconsistent with any other provisions, or in any manner not
adversely affecting the interests of the holders of the Rights.

          Copies of the Rights Agreement and the Amendment have been filed with
the Securities and Exchange Commission as an Exhibit to a Registration Statement
on Form 8-A and a Form 8-A/A.  A copy of the Rights Agreement and the Amendment
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 and the Amendment, which are incorporated
herein by reference.

                                       7