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                                                                     EXHIBIT 4.4

                             BOIS D'ARC ENERGY, LLC
                             600 TRAVIS, SUITE 6275
                              HOUSTON, TEXAS 77002

as of July 21, 2004

Ms. Sally Lynn Blackie
BetsWest Interests, L.P.
5900 Highway 290 East
Brenham, Texas 77833

      Re:   Bois d'Arc Energy, LLC Contribution Agreement
            Supplemental Agreement

Dear Ms. Blackie:

      Bois d'Arc Energy, LLC (the "Company") has offered to you and/or your
limited partnership BetsWest Interests, L.P. ("BetsWest") the opportunity to
contribute the working interest you and/or BetsWest own in offshore Gulf of
Mexico oil and gas leases to Bois d'Arc Properties, LP, a wholly owned
subsidiary of the Company, in return for the issuance of membership units in the
Company. The details and mechanics of this proposed transaction are set forth in
the Contribution Agreement and Private Place Memorandum previously delivered to
you. Capitalized terms used herein and not otherwise defined will have the
meanings assigned to such terms in the Contribution Agreement.

      You and the Company hereby agree as follows:

      1.    (a)   If the Company determines to register under the Securities
Act shares of common stock of the Company (as converted to a corporation as
provided in Section 17.6 of the Operating Agreement) for its own account and
pursuant to an initial public offering, the Company shall use its reasonable
best efforts to include in such registration the shares issued to you pursuant
to the conversion, as you request, but not to exceed 50% of the number of shares
so issued to you on the same terms and conditions as shares of common stock
offered by the Company for its own account. You will be required to give the
Company written notice of the number of shares you so desire to register within
30 days after the date the Company notifies you of its intent to effect a
registration. If the Company's underwriters advise the Company that in their
reasonable opinion the number of shares requested to be included in such
registration exceeds the number which can be sold in the offering without
adversely affecting the marketability of the offering, the number of shares to
be included by you will be reduced accordingly prior to any reductions by the
Company. If any other holder of common stock has registration rights and such
holder (or holders) has exercised its (or their) registration rights, the number
of shares to be included by such other holder (or holders) will be reduced prior
to any reduction in the number of shares to be included by you. You agree to
execute and deliver all agreements that may be requested by the Company or the
underwriters that are customary for

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Ms. Sally Lynn Blackie
as of July 21, 2004
Page 2

selling shareholders in a transaction of this nature. If the Company determines
not proceed with a registration, it shall be relieved of any further obligation
under this Section 1.

            (b)   The Company shall (i) furnish to you such number of copies of
such registration statement, each amendment and supplement thereto, the
prospectus included in such registration statement (including, without
limitation, each preliminary prospectus) and such other documents as you may
reasonably request in order to facilitate the disposition of your common stock
of the Company, (ii) use its reasonable best efforts to cause all such common
stock to be listed on each securities exchange or exchanges or automated
quotation system upon which securities of the Company of the same class are then
listed, and (iii) use its reasonable best efforts to comply with all applicable
rules and regulations of the Securities and Exchange Commission and applicable
state securities authorities.

            (c)   You will be responsible for your own legal fees incurred in
connection with the offering.

            (d)   The Company agrees to indemnify and hold harmless you and
BetsWest from and against any and all losses, claims, damages and liabilities
(including, without limitation, reasonable legal fees and other expenses
incurred in connection with any suit, action or proceeding or any claim
asserted), arising out of any untrue statement or alleged untrue statement of a
material fact contained in the registration statement or any prospectus, or
arising out of any omission or alleged omission to state therein a material fact
required to be stated therein or necessary in order to make the statements
therein, in the light of the circumstances under which they were made, not
misleading, except insofar as such losses, claims, damages or liabilities arise
out of any untrue statement or omission or alleged untrue statement or omission
made in reliance upon and in conformity with any information relating to you
furnished to the Company in writing by you expressly for use therein.

            (e)   You agree to indemnify and hold harmless the Company and its
affiliates (and their officers and directors (or analogous principals)) from and
against any and all losses, claims, damages and liabilities (including, without
limitation, reasonable legal fees and other expenses incurred in connection with
any suit, action or proceeding or any claim asserted), arising out of any untrue
statement or alleged untrue statement of a material fact contained in the
registration statement or any prospectus, or arising out of any omission or
alleged omission to state therein a material fact required to be stated therein
or necessary in order to make the statements therein, in the light of the
circumstances under which they were made, not misleading, insofar as such
losses, claims, damages or liabilities arise out of any untrue statement or
omission or alleged untrue statement or omission made in reliance upon and in
conformity with any information relating to you furnished to the Company in
writing by you expressly for use therein.

      2.    This supplemental agreement constitutes the entire agreement and
understanding of the parties hereto with respect to the subject matters hereof
and supersedes any and all prior and contemporaneous negotiations, agreements,
arrangements and understandings between the

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Ms. Sally Lynn Blackie
as of July 21, 2004
Page 3

parties, written or oral, relating to the matters provided for herein, including
without limitation, the matters set forth in paragraph 9 of the letter agreement
dated July 21, 2004 among you, the Company and certain other persons, provided
the remaining terms of such letter agreement, including paragraphs 1-8 thereof,
remain in full force and effect.

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Ms. Sally Lynn Blackie
as of July 21, 2004
Page 4

      The Company encourages you to discuss this supplemental agreement with
your attorneys and counselors. This agreement will be effective upon execution
by all parties hereto and shall be effective as of July 1, 2004. This agreement
may be executed in multiple counterparts, all of which together shall constitute
one instrument.

                                   Sincerely,

                                   BOIS D'ARC ENERGY, LLC

                                   By: /s/ Roland O. Burns
                                       -----------------------------------------
                                       Roland O. Burns,
                                       Senior Vice President and Chief Financial
                                       Officer

cc:   Gary W. Blackie, President

Agreed and Accepted:

/s/ Sally L. Blackie
--------------------------------
Sally Lynn Blackie, Individually

BETSWEST INTERESTS, L.P.

By: JO Arc Resources, Inc.,
   ------------------------
   general partner

By: /s/ Sally L. Blackie
   -----------------------------
   Sally Lynn Blackie, President