<PAGE>
                                                                    EXHIBIT 10.7

                   [MILLER EXPLORATION COMPANY - LETTERHEAD]


                                 May 27, 1999


Mr. C.E. "Gene" Miller
Eagle Investment Inc.
3140 Logan Valley Road
Traverse City, MI 49685

        RE:     April 1, 1999 Purchase Letter Agreement
                Bank of Montreal Credit Agreement


Dear Gene,

        As per that certain Purchase Letter Agreement date April 1, 1999 Eagle
Investments, Inc. ("Eagle") agreed to acquire up to $6 million worth of Miller
Exploration Company "(MEXP") properties. As a result of the sale by MEXP of
certain non-operated properties, Eagle will be required to purchase $2.9 million
worth of MEXP properties. Exhibit "A" sets out Eagle's working interest in the
specific properties for which it will be acquiring. Eagle's acquisition is
subject to the terms and conditions of the April 1,1999 Purchase Letter
Agreement, a copy of which is attached.

        Eagle and MEXP further agree that the following additional terms and
conditions will apply to Eagle's acquisition.

                1.      MEXP will retain all of its rights within the existing
                        producing wellbores at Dry Creek, Moselle, and
                        Centerville Domes. In the event a new well is proposed
                        (other than a substitute well due to, but not limited to
                        mechanical difficulties) in the existing units or the
                        existing well is redrilled to a new bottomhole location,
                        Eagle will have the right to participate for its working
                        interest share.

                2.      Eagle will have the option to participate for its
                        working interest share in all leasehold acquisitions on
                        the subject domes subsequent to June 1, 1999.

                3.      Eagle will pay its allocated share of operating and
                        processing expenses and necessary facility enhancement
                        expenses. It is expressly understood that MEXP is not
                        selling any interest in any existing facilities or
                        pipelines.

                4.      The applicable existing Joint Venture Agreements and
                        Joint Operating Agreements will govern all operations on
                        the subject domes.

                5.      Eagle will have a restricted license to the proprietary
                        3-D seismic data covering Richmond, Grange, and Arm
                        Domes. Eagle will have the right to review in MEXP's
                        office, but will not be granted a license on the 3-D
                        seismic data covering the Interdomal, Centerville,
                        Moselle, and Kola Domes and will be subject to the terms
                        and conditions under the applicable license agreements
                        owned by MEXP on these domes.

                6.      MEXP is currently discussing the sale of additional
                        interest in these prospects under the same terms and
                        conditions to the third parties. In the event MEXP sells
                        this program to a third party for less consideration,
                        Eagle will have the right to participate
                        proportionately for those same terms and condition.
<PAGE>



                                                Sincerely,

                                                MILLER EXPLORATION COMPANY



AGREED TO AND ACCEPTED THIS 27th DAY OF MAY, 1999.

EAGLE INVESTMENTS INC.

BY:/s/ C.E. Miller
   ------------------------------
C.E. ("Gene") Miller-President





                                      -2-

<PAGE>



                                  Exhibit "A"
         attached to that certain Letter Agreement dated May 27, 1999
         between Eagle Investment, Inc and Miller Exploration Company


                                 WI%               Eagle's         Eagle's
    Dome        County        Available         Participation        WI%
-------------------------------------------------------------------------------
    Arm        Lawrence         28.33%              42.33%         11.99%
   Grange      Lawrence         28.33%              42.33%         11.99%
    Kola       Covington        20.30%              42.33%          8.59%
 Richmond      Covington        35.00%              42.33%         14.82%
 Dry Creek     Covington        44.58%              42.33%         18.87%
Centerville      Jones          22.80%              42.33%          9.65%
  Moselle        Jones          50.00%              42.33%         21.17%
 Interdomal   Jones/Covington   50.00%              42.33%         21.17%
   Don't       Covington        25.00%              42.33%         10.58%
 Eminence      Covington        10.00%              42.33%          4.23%


5/25/99
$2.9mm