<PAGE>   1
                                  Exhibit 10.4

                         Deferred Compensation Agreement
            and Stock Sale Lock-Up Agreement (Michael D. Herrington)



<PAGE>   2



DEFFERED COMPENSATION AGREEMENT


         This Agreement is entered into by and between Lone Star International
Energy, Inc., hereinafter referred to as "Employer", and Michael D. Herrington,
P. O. Box 701 Breckenridge, TX 76424, hereinafter referred to as "Employee", to
be effective as of January 7, 1997.

         WHEREAS, effective January 7, 1997, Employee commenced employment with
Employer pursuant to an Employment Contract, the terms of which are incorporated
herein by this reference; and,

         WHEREAS, the Parties agree that said Employment Contract provides for a
compensation level for Employee in the amount of $120,000.00 per annum; and,

         WHEREAS, the Parties agree that Employer is unable to meet the full
compensation level provided in the Employment Contract, and Employee
acknowledges that this fact was know and accepted by Employee at the time said
contract was negotiated and entered into; and,

         WHEREAS, the Parties wish to define the actual cash compensation that
will be paid to Employee, and to provide the terms for the deferral of a portion
of the compensation required under the Employment Contract.

         NOW THEREFORE, the Parties hereto agree as follows:

Employer agrees to pay and Employee agrees to accept as the cash portion of the
compensation, the total of $38,958.34 annually, to be paid in twenty (20)
payments of $1,947.92 each. Said payments are to made in arrears, in accordance
with Employer's normal and customary payroll periods of the 1st and 15th of each
month, commencing in March, 1997.

The balance of the compensation required under the Employment Contract, being a
total of $81,041.66 shall be deferred by Employee, with the obligation of
Employer being evidenced by a Note, the form and substance of which is attached
hereto as Exhibit "A". The Note covering such deferred compensation shall be
issued to Employee at the end of each calendar year, representing the total
amount deferred during the Employer's annual accounting period.

It is understood by the Parties, that at such time, and in the event Employer is
able to pay the total compensation required under the Employment Contract, the
cash compensation may be increased in order to comply with such agreement. The
Employee may, however, with the consent of Employer elect to continue the
deferral of all or any portion of the required compensation, and to continue to
accept a Note Payable by Employer as described herein.
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This Agreement shall be deemed an addendum to the Employment Contract between
the Parties, and shall be incorporated therein by this reference. This Agreement
may also be amended from time to time to reflect increases in the cash portion
of the compensation as may be agreed by the parties.

The laws of the State of Texas shall govern this Agreement.

IN WITNESS WHEREOF, the Parties have executed this Agreement to become effective
as herein above first mentioned.

                                       EMPLOYER

                                       Lone Star International Energy, Inc.


                                       -----------------------------------------
                                       C. E. Justice, Chairman


                                            EMPLOYEE


                                            ------------------------------------
                                            Michael D. Herrington




<PAGE>   4



ADDENDUM TO DEFERRED COMPENSATION AGREEMENT


         This Addendum is being entered into between Lone Star International
Energy, Inc. ("Employer") and Michael D. Herrington ("Employee"), to be
effective for all purposes as of January 1, 1998.

RECITALS

         WHEREAS, the parties hereto entered into a Deferred Compensation
Agreement effective as of January 7, 1997, whereby the Employee agreed to defer
a portion of the compensation due pursuant to an Employment Contract with
Employer; and,

         WHEREAS, the Deferred Compensation Agreement referenced herein covered
the compensation period of 1997, and the Parties wish to amend the Agreement so
as to provide for the deferred amounts for the 1998 compensation period of the
Employment Contract.

         NOW THEREFORE, the Parties hereby agree as follows:

Commencing January 1, 1998 and continuing on a month to month basis until
further amended by mutual agreement of the parties, Employee agrees to accept a
total of $3,750.00 per month payable in equal payments on the 1st and 15th of
each month, and to defer the balance of $6,750.00 per month as required under
the subject Employment Contract.

As required by the referenced Deferred Compensation Agreement, the deferred
compensation as stipulated in paragraph 1 shall be evidenced by a Note Payable
with interest, to be executed by the Employer in favor of the Employee on a
quarterly basis.

All other terms and provisions of the subject Deferred Compensation Agreement
shall remain in full force and effect.

This Addendum shall be attached to and become a part of the Deferred
Compensation Agreement upon execution by the Parties.

IN WITNESS WHEREOF, the parties have executed this Addendum to become effective
as of January 1, 1998.

Lone Star International Energy, Inc.                       Employee:


------------------------------                             ---------------------
C. E. Justice                                              Michael D. Herrington
Chairman, CEO


<PAGE>   5



                          STOCK SALE LOCK-UP AGREEMENT


         This Agreement is entered into by and between Lone Star International
Energy, Inc., 528 Grant Road, Mineral Wells, Texas 76067 (hereinafter referred
to as "Lone Star"), and Michael D. Herrington, (hereinafter referred to as
"Employee"), to be effective as hereinafter stipulated.

                                    RECITALS

         WHEREAS, Lone Star is the maker of certain Note(s) Payable to Employee,
representing a portion of Employee's salary compensation that by prior agreement
was deferred, with said deferred salary incurring interest also payable to
Employee; and,


         WHEREAS, Lone Star is currently carrying the Note(s) Payable to
Employee as a long term liability of the company reflected in its audited
financial statements; and,

         WHEREAS, Lone Star desires to clear all or a portion of its long term
debt as reflected in its audited financial statements, but is currently unable
to meet the cash requirements necessary to pay the referenced Note(s) Payable;
and,

         WHEREAS, Employee desires to assist Lone Star in eliminating portions
of its long term debt, and is confident in the direction and development of the
company to the extent Employee is willing to liquidate the Note(s) Payable for
common stock rather than cash.

         NOW THEREFORE, in consideration of the benefits to be derived by the
Parties hereto, it is agreed as follows:

         1.       Lone Star agrees to issue to Employee the total of 323,185
                  shares of its common stock as full and complete satisfaction
                  of the Note(s) Payable attached hereto as an Exhibit, and
                  incorporated herein by this reference.


         2.       Lone Star agrees to prepare and secure the registration of the
                  common stock hereby issued through the utilization of an S-8
                  Registration as allowed under the Securities Exchange Act and
                  the corresponding Rules and Regulations of the Securities
                  Exchange Commission. Upon completion of said S-8 Registration,
                  the shares of common stock will be free trading, with no
                  further restrictions except as contained herein.

         3.       Lone Star acknowledges that its has obtained the requisite
                  Board of Directors approval to enter into this Agreement and
                  to issue the subject shares of common stock and to register
                  the same pursuant to an S-8 Registration.

         4.       Employee agrees that upon receipt of the common stock in lieu
                  of cash settlement of the Note(s) Payable, he will not attempt
                  to liquidate the shares into the market except as follows:
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                  a.       Employee agrees to hold all shares received hereunder
                           for a period of sixty (60) days from the date of
                           issue.

                  b.       After the initial 60 day holding period, an amount of
                           such shares as may be necessary to satisfy cash
                           requirements for any income tax liability that may be
                           incurred as a result of this transaction.

                  c.       After the initial 60 day holding period, not more
                           than One Quarter (1/4) of the total amount of shares
                           issued hereunder in any given calendar quarter after
                           expiration of the holding period.

         5.       Notwithstanding the foregoing, Employee agrees that prior to
                  any proposed sale of the shares of common stock subject to
                  this Agreement, either into the public market or through a
                  private transaction, he will notify Lone Star of his intent to
                  sell. Such notice to include the total number of shares
                  proposed for sale together with the share price per share for
                  the transaction. Upon receipt of the notice of intent to sell
                  from Employee, Employee agrees to give Lone Star the option
                  for 72 hours to match the terms of the proposed sale and
                  redeem the subject shares for retirement by the company. After
                  the expiration of the 72-hour option period, if Lone Star has
                  not elected to match the sale terms, the Employee may either
                  complete the proposed sale or retain the shares at his sole
                  election.

         6.       After the expiration of one year from the end of the 60
                  holding period referenced in paragraph 4 above, the Parties
                  agree that all restrictions as to volume limits on the sale of
                  the subject shares shall expire. Thereafter, Employee may
                  dispose of all remaining shares at his sole discretion.
                  Employee does however, confirm that the notice and option
                  provisions described in paragraph 5 shall remain in effect for
                  so long as Employee remains in the employment of Lone Star or
                  one of its subsidiaries.

         7.       The laws of the State of Texas shall govern this Agreement,
                  and any disputes that may arise shall be submitted to
                  arbitration with venue in Tarrant County, Texas. The Parties
                  agree that any ruling made through the arbitration procedures
                  in effect in Tarrant County, Texas shall be binding so as to
                  resolve any matters in controversy.



                                                                               2
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         IN WITNESS WHEREOF, the parties have executed this Agreement on the
dates so indicated, to be effective for all purposes as of April 1, 1998.

                                            Lone Star International Energy, Inc.


                                            /s/ Richard Baker, President
                                            Date: April 22, 1998



                                            Employee:


                                            /s/ Michael D. Herrington
                                            Date: April 23, 1998



                                                                               3
<PAGE>   8



                                 PROMISSORY NOTE


WEATHERFORD, TEXAS                                         DECEMBER 31, 1997


         For value received, the undersigned, LONE STAR INTERNATIONAL ENERGY,
INC., 200 Palo Pinto, Suite 108, Weatherford, Texas 76086, hereinafter referred
to as "Maker", promises to pay Michael D. Herrington, hereinafter referred to as
"Holder", the sum of Eighty One Thousand, and Forty Two Dollars ($81,042.00), in
lawful and legal tender of the United States of America, payable as stated
hereinbelow:

1.       Payment is due and payable on or before December 30, 1998, unless
         extended by Holder. Any such extension to be evidenced in writing and
         executed by Holder.

2.       This Promissory Note shall bear interest at the rate of Eight and One
         Quarter Percent (8 1/4%) per annum.

3.       There shall be no prepayment penalty should Maker elect to discharge
         this note prior to maturity.

4.       Holder has the exclusive option to elect to take (a) cash payment in
         full (b) restricted common stock of Maker in lieu of cash, or (c) a
         combination of cash and restricted common stock as satisfaction of this
         note. In the event Holder elects to take all or partial payment in
         restricted common stock of Maker, said stock shall be valued for
         purposes of this note, at fifty percent (50%) of the closing bid price
         for such shares, as quoted on the publicly traded market for which said
         shares are listed.

         IN WITNESS WHEREOF, the undersigned has executed this note to be
effective as of the date first above written.

                                       Lone Star International Energy, Inc.



                                       /s/ Don R. Pyles
                                       Sr. VP, General Counsel





<PAGE>   9



                                 PROMISSORY NOTE



MINERAL WELLS, TEXAS                                       MARCH 31, 1998



For value received, the undersigned, LONE STAR INTERNATIONAL ENERGY, INC., 528
Grant Road, Mineral Wells, Texas 76067, hereinafter referred to as "Maker",
promises to pay Michael D. Herrington, hereinafter referred to as "Holder", the
sum of Twenty Thousand Two Hundred and Fifty Dollars ($22,250.00), in lawful and
legal tender of the United States of America, payable as stated hereinbelow:

1.       Payment is due and payable on or before December 30, 1998, unless
         extended by holder. Any such extension to be evidenced in writing and
         executed by Holder.

2.       This Promissory Note shall bear interest at the rate of Eight and One
         Quarter Percent (8 1/4%) per annum.

3.       There shall be no prepayment penalty should Maker elect to discharge
         this note prior to maturity.

4.       Holder has the exclusive option to elect to take (a) cash payment in
         full (b) restricted common stock of the Maker in lieu of cash, or (c) a
         combination of cash and restricted common stock as satisfaction of this
         note. In the event Holder elects to take all or partial payment in
         restricted common stock of Maker, said stock shall be valued for
         purposes of this note, at fifty percent (50%) of the closing bid price
         for such shares, as quoted on the publicly traded market for which said
         shares are listed.

         IN WITNESS WHEREOF, the undersigned has executed this note to be
effective as of the date first above written.

                                       Lone Star International Energy, Inc.


                                       /s/ Don R. Pyles
                                       Sr. VP, General Counsel