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                                                                    EXHIBIT 10.4


                                 PROMISSORY NOTE

$10,000,000                   Lafayette, Louisiana             December 21, 2000

      FOR VALUE RECEIVED, the undersigned, PetroQuest Energy, Inc., a Louisiana
corporation, and PetroQuest Energy One, L.L.C., a Louisiana limited liability
company (herein collectively called "Borrower"), hereby jointly, severally, and
solidarily promise to pay to the order of EnCap Energy Capital Fund III, L.P.
(herein called "Lender"), the principal sum of Ten Million Dollars
($10,000,000), or, if greater or less, the aggregate unpaid principal amount of
the Advances made under this Note by Lender to Borrower pursuant to the terms of
this Credit Agreement (as hereinafter defined), together with interest on the
unpaid principal balance thereof as hereinafter set forth, both principal and
interest payable as herein provided in lawful money of the United States of
America at the offices of Hibernia National Bank, 313 Carondelet Street, New
Orleans Louisiana, or at such other place within Orleans Parish, Louisiana, as
from time to time may be designated by the holder of this Note.

      This Note (a) is issued and delivered under that certain Credit Agreement
of even date herewith among Borrower, PetroQuest Energy, Inc., a Delaware
corporation, and Lender (herein, as from time to time supplemented, amended or
restated, called the "Credit Agreement"), and is a "Note" as defined therein,
(b) is subject to the terms and provisions of the Credit Agreement, which
contains provisions for payments and prepayments hereunder and acceleration of
the maturity hereof upon the happening of certain stated events. Payments on
this Note shall be made and applied as provided herein and in the Credit
Agreement. Reference is hereby made to the Credit Agreement for a description of
certain rights, limitations of rights, obligations and duties of the parties
hereto and for the meanings assigned to terms used and not defined herein.

      The principal amount of this Note, together with all interest accrued
hereon, shall be due and payable in full on the Maturity Date. Interest payments
on this Note are due on each Quarterly Payment Date, beginning March 30, 2001.

      The principal amount of this Note (exclusive of any past due principal or
interest) from time to time outstanding shall bear interest on each day
outstanding at the Base Rate in effect on such day; provided that if an Event of
Default has occurred and is continuing, the principal amount of this Note
(exclusive of any past due principal or interest) from time to time outstanding
shall bear interest on each day outstanding at the Default Rate in effect on
such day. All past due principal and interest on the Loan shall bear interest on
each day outstanding at the Default Rate in effect on such day, and such
interest shall be due and payable daily as it accrues.

      Notwithstanding the foregoing paragraph and all other provisions of this
Note or any other Loan Document, in no event shall the interest payable hereon,
together with any other amounts constituting interest on the Obligations,
whether before or after maturity, exceed the maximum amount of interest which,
under applicable law, may be charged on this Note and such other
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Obligations, and this Note is expressly made subject to the provisions of the
Credit Agreement which more fully set out the limitations on how interest
accrues hereon. The term "applicable law" as used in this Note shall mean the
Laws of the State of Louisiana including the Laws of the United States, as such
laws now exist or may be changed or amended or come into effect in the future.

      If this Note is placed in the hands of an attorney for collection after
default, or if all or any part of the indebtedness represented hereby is proved,
established or collected in any court or in any bankruptcy, receivership, debtor
relief, probate or other court proceedings, Borrower and all endorsers, sureties
and guarantors of this Note jointly and severally agree to pay reasonable
attorneys' fees and collection costs to the holder hereof in addition to the
principal and interest payable hereunder.

      Borrower and all endorsers, sureties and guarantors of this Note hereby
severally waive demand, presentment, notice of demand and of dishonor and
nonpayment of this Note, protest, notice of protest, notice of intention to
accelerate the maturity of this Note, declaration or notice of acceleration of
the maturity of this Note, diligence in collecting, the bringing of any suit
against any party and any notice of or defense on account of any extensions,
renewals, partial payments or changes in any manner of or in this Note or in any
of its terms, provisions and covenants, or any releases or substitutions of any
security, or any delay, indulgence or other act of any trustee or any holder
hereof, whether before or after maturity.

      THIS NOTE AND THE RIGHTS AND DUTIES OF THE PARTIES HERETO SHALL BE
GOVERNED BY THE LAWS OF THE STATE OF LOUISIANA (WITHOUT REGARD TO PRINCIPLES OF
CONFLICTS OF LAW), EXCEPT TO THE EXTENT THE SAME ARE GOVERNED BY APPLICABLE
FEDERAL LAW.


                                    PETROQUEST ENERGY, INC.,a Louisiana
                                    corporation

                                    By: /s/ Charles T. Goodson
                                        ----------------------------------------
                                        Name:  Charles T. Goodson
                                        Title: Chairman of the Board and Chief
                                               Executive Officer


                                    PETROQUEST ENERGY ONE, L.L.C., a
                                    Louisiana limited liability company

                                    By: PETROQUEST ENERGY, INC., a
                                        Louisiana corporation, its sole member

                                        By: /s/ Charles T. Goodson
                                            ------------------------------------
                                            Name:  Charles T. Goodson
                                            Title: Chairman of the Board and
                                                   Chief Executive Officer