Document:

<PAGE>

                                                                    Exhibit 10.3

                         REGISTRATION RIGHTS AGREEMENT

     This Registration Rights Agreement (this "Agreement") is entered into as of
                                               ---------
July 11, 2000, by and among Miller Exploration Company, a Delaware corporation
(the "Company"), and Guardian Energy Management Corp., a Michigan corporation
      -------
(the "Purchaser").
      --------

                                   RECITALS:
                                   --------

     A.   The Company and the Purchaser have entered into that certain
Securities Purchase Agreement of even date herewith (the "Purchase Agreement"),
                                                          ------------------
pursuant to which the Purchaser is acquiring a convertible promissory note (the
"Note") and certain warrants (the "Warrants") that are convertible into and
 ----                              --------
exercisable for shares (the "Shares") of the Company's common stock, par value
                             ------
$.01 per share ("Common Stock").
                 ------------

     B.   Pursuant to the terms of the Purchase Agreement, the Company has
agreed to register the shares of Common Stock received by the Purchaser pursuant
to the terms and conditions set forth herein.

                                  AGREEMENTS:
                                  ----------

     NOW, THEREFORE, for valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, the parties hereto agree as follows:

     1.   Definitions.  As used herein, the following terms shall have the
          -----------
meanings indicated.

          "Commission" means the Securities and Exchange Commission.
           ----------

          "Exchange Act" means the Securities Exchange Act of 1934, as amended.
           ------------

          "Registrable Securities" means the shares of Common Stock received by
           ----------------------
the Purchaser pursuant to conversion of the Note and the exercise of the
Warrants and held of record by the Purchaser.  Any Registrable Security will
cease to be a Registrable Security when a registration statement under the
Securities Act covering such Registrable Security has been declared effective by
the Commission or when such Registrable Security is no longer held of record by
the Purchaser.

          "Securities Act" means the Securities Act of 1933, as amended.
           --------------

     2.   Shelf Registration Statement.  (a)  The Company will upon written
          ----------------------------
request from the Purchaser file a "shelf" registration statement on Form S-3
pursuant to Rule 415 under the Securities Act (the "Shelf Registration
                                                    ------------------
Statement"), with respect to the sale of the Registrable Securities.  The
Company shall use all commercially reasonable efforts to have the Shelf
Registration Statement
<PAGE>

declared effective by the Commission under the Securities Act as promptly as
practicable thereafter and to keep the Shelf Registration Statement effective
for a period of 180 days. The Company's obligations with respect to the Shelf
Registration Statement shall be subject to the limitations set forth below.

          (b) Notwithstanding the foregoing, if the Company shall furnish to the
Purchaser a certificate signed by the President of the Company stating that in
good faith judgment of the Board of Directors of the Company, it would be
seriously detrimental to the Company and its stockholders for a Shelf
Registration Statement to be filed and it is therefore essential to defer the
filing of such registration statement, the Company shall have the right to defer
such filing for a period of not more than 180 days after receipt of the request
of the Purchaser; provided, however, that the Company many not utilize this
                  --------  -------
right more than once in any twelve-month period.

          (c)  In addition and without limitation, the Company shall not be
obligated to effect, or to take any action to effect, any registration pursuant
to this Section 2;
        ---------

               (i)  After the Company has effected three registrations requested
     by the Purchaser pursuant to this Section 2 and such registrations have
                                       ---------
     been declared or ordered effective; or

               (ii) During the period starting with the date 60 days prior to
     the Company's good faith estimate of the date of filing of, and ending on a
     date 90 days after the effective date of, a registration subject to Section
                                                                         -------
     3 hereof; provided that the Company is actively employing in good faith all
     -
     commercially reasonable efforts to cause such registration statement to
     become effective.

          (d)  It shall be a condition precedent to the obligations of the
Company to take any action pursuant to this Section 2 with respect to the
                                            ---------
Registrable Securities of the Purchaser that the Purchaser furnish to the
Company such information regarding itself, the Registrable Securities held by
it, and the intended method of disposition of such securities as shall be
required to effect the registration of such Holder's Registrable Securities.

     3.   Piggyback Registration.
          ----------------------

          (a) Right to Piggyback.  If at any time the Company proposes to file a
              ------------------
registration statement under the Securities Act with respect to an offering of
Common Stock (except (i) on Form S-4, Form S-8 or any successor form thereto or
(ii) with respect to a distribution solely to existing stockholders of the
Company), whether or not for its own account, then the Company shall give
written notice of such proposed filing to the Purchaser at least 20 days before
the anticipated filing date (the "Piggyback Notice").  The Piggyback Notice
                                  ----------------
shall offer such holders the opportunity to register such amount of Registrable
Securities as the purchaser may request (a "Piggyback Registration").  Subject
                                            ----------------------
to Section 3(b) hereof, the Company shall include in each such Piggyback
   ------------
Registration all Registrable Securities requested to be included in the
registration for such offering. The Purchaser shall be permitted to withdraw all
or part of the Registrable Securities from a Piggyback Registration at any time
prior to the effective date of such Piggyback Registration.

                                      -2-
<PAGE>

          (b)  Priority on Piggyback Registrations.  The Company shall use
               -----------------------------------
commercially reasonable efforts to cause the managing underwriters of a proposed
underwritten offering of Common Stock to permit holders of Registrable
Securities requested to be included in the registration for such offering to
include all such Registrable Securities on the same terms and conditions as any
similar equity securities, if any, of the Company included therein.
Notwithstanding the foregoing, if the managing underwriters of such underwritten
offering determine in good faith that the total number of securities that such
holders, the Company, and any other persons having rights to participate in such
registration, propose to include in such offering is such as to materially and
adversely affect the success of such offering, then (x) if such Piggyback
Registration is a primary registration on behalf of the Company, the securities
to be offered (i) for the Purchaser and (ii) for the account of all other
persons other than the Company shall be reduced or limited pro rata in
                                                           --- ----
proportion to the respective dollar amounts of securities owned to the extent
necessary to reduce the total number of securities to be included in such
offering to the amount recommended by such managing underwriters, and (y) if
such Piggyback Registration is an underwritten secondary registration on behalf
of holders of equity securities of the Company, the Company shall include in
such registration:  (A) first, up to the full number of securities of such
persons exercising "demand" registration rights that in the opinion of such
underwriter can be sold (allocated among such holders as they may so determine),
and (B) second, the number of Registrable Securities included in such
registration pursuant to this Section 3 or "piggy-back" registration rights
                              ---------
contained in the other registration rights agreements in excess of the
securities such persons exercising "demand" registration rights propose to sell
that, in the opinion of such managing underwriter, can be sold without
materially and adversely affecting such offering (allocated pro rata on the
                                                            --- ----
basis of the aggregate dollar amount of securities owned).

     Notwithstanding the foregoing, to the extent that the priority provisions
set forth in this Section 3(b) are inconsistent with the priority provisions set
                  ------------
forth in any existing Registration Rights Agreements of the Company, then the
priority provisions contained in such Registration Rights Agreements will
control with respect to the shares of Common Stock requested to be included
pursuant to such Registration Rights Agreements. The provisions of this
paragraph shall not increase the number of Registrable Securities that a holder
could otherwise include pursuant to this Section 3 by reason of the allocation
                                         ---------
contained in the immediately preceding paragraph.

     4.   Registration Procedures.
          -----------------------

     The Company will as expeditiously as reasonably possible:

          (a)  furnish to the Purchaser, prior to filing the Shelf Registration
Statement, if requested in writing, copies of the Shelf Registration Statement
as proposed to be filed, and thereafter furnish to the Purchaser such number of
copies of the Shelf Registration Statement, each amendment and supplement
thereto (in each case including all exhibits thereto), the prospectus included
in the Shelf Registration Statement (including each preliminary prospectus) and
such other documents as the Purchaser may reasonably request in writing in order
to facilitate the disposition of the Registrable Securities owned by the
Purchaser;

                                      -3-
<PAGE>

          (b)  use all commercially reasonable efforts to register or qualify
the Registrable Securities under such other securities or blue sky laws of such
jurisdictions as the Purchaser may reasonably request and do any and all other
acts and things which may be reasonably necessary to enable the Purchaser to
consummate the disposition in such jurisdictions of the Registrable Securities;
provided that the Company will not be required to (i) qualify generally to do
--------
business in any jurisdiction where it would not otherwise be required to qualify
but for this subsection, (ii) subject itself to taxation in any such
jurisdiction or (iii) consent to general service of process in any such
jurisdiction;

          (c)  notify the Purchaser, at any time when a prospectus relating
thereto is required to be delivered under the Securities Act, of the occurrence
of an event requiring the preparation of a supplement or amendment to such
prospectus so that, as thereafter delivered to the purchasers of the Registrable
Securities, such prospectus will not contain an untrue statement of a material
fact or omit to state any material fact required to be stated therein or
necessary to make the statements therein not misleading and promptly make
available to the Purchaser any such supplement or amendment; and

          (d)  make available for inspection by the Purchaser and any attorney,
accountant or other professional retained thereby (collectively, the
"Inspectors"), all financial and other records, pertinent corporate documents
 ----------
and properties of the Company (collectively, the "Records") as shall be
                                                  -------
reasonably necessary to enable them to exercise their due diligence
responsibility, and cause the Company's officers, directors and employees to
supply all information reasonably requested by any such Inspectors in connection
with the Shelf Registration Statement.  Records which the Company determines, in
good faith, to be confidential and which it notifies the Inspectors are
confidential shall not be disclosed by the Inspectors unless (i) in the judgment
of counsel to the Company the disclosure of such Records is necessary to avoid
or correct a misstatement or omission in the Registration Statement or (ii) the
release of such Records is ordered pursuant to a subpoena or other order from a
court of competent jurisdiction.  The Purchaser agrees that information obtained
by it as a result of such inspections shall be deemed confidential and shall not
be used by it as the basis for any market transactions in the securities of the
Company unless and until such is made generally available to the public.  The
Purchaser further agrees that it will, upon learning that disclosure of such
Records is sought in a court of competent jurisdiction, give notice to the
Company and allow the Company, at its expense, to undertake appropriate action
to prevent disclosure of the Records deemed confidential.

     The Company may require the Purchaser to promptly furnish in writing to the
Company such information regarding the distribution of the Registrable
Securities as it may from time to time reasonably request and such other
information as may be legally required in connection with such registration.

     The Purchaser agrees that, upon receipt of any notice from the Company of
the happening of any event of the kind described in Section 4(c) hereof,
                                                    ------------
Purchaser will immediately discontinue disposition of Registrable Securities
pursuant to the Registration Statement until the Purchaser's receipt of the
copies of the supplemented or amended prospectus contemplated by Section 4(c)
                                                                 ------------
hereof, and, if so directed by the Company, the Purchaser will deliver to the
Company all copies,

                                      -4-
<PAGE>

other than permanent file copies then in the Purchaser's possession, of the most
recent prospectus covering such Registrable Securities at the time of receipt of
such notice. If the Company shall give such notice, the Company shall extend the
period during which the Registration Statement shall be maintained effective by
the number of days during the period from and including the date of the giving
of notice pursuant to Section 4(c) hereof to the date when the Company shall
make available to the Purchaser a prospectus supplemented or amended to conform
with the requirements of Section 4(c) hereof. The Purchaser acknowledges that
the delivery of any such notice shall constitute material non-public information
and agrees that it shall keep the existence of such notice confidential.

     5.   Registration Expenses.
          ---------------------

     In connection with the Registration Statement required to be filed
hereunder, the Company shall pay the following registration expenses:  (a) all
registration and filing fees; (b) the fees and expenses of the Company's
compliance with securities or blue sky laws (including reasonable fees and
disbursements of counsel in connection with blue sky qualifications of the
Registrable Securities); (c) printing expenses; (d) the reasonable fees and
disbursements of counsel for the Company and the customary fees and expenses for
independent certified public accountants retained by the Company; and (e) the
reasonable fees and expenses of any special experts retained by the Company in
connection with such registration.  The Company shall not have any obligation to
pay any legal fees of the Purchaser, any underwriting fees, discounts or
commissions attributable to the sale of Registrable Securities or any out-of-
pocket expenses of the Purchaser (or its agents).

     6.   Indemnification; Contribution.
          -----------------------------

          (a)  Indemnification by the Company.  The Company agrees to indemnify
               ------------------------------
and hold harmless the Purchaser from and against any and all losses, claims,
damages, liabilities and expenses (including reasonable costs of investigation)
arising out of or based upon any untrue statement or alleged untrue statement of
a material fact contained in the Registration Statement or prospectus contained
therein or in any amendment or supplement thereto or in any preliminary
prospectus, or arising out of or based upon any omission or alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein not misleading, except insofar as such losses, claims,
damages, liabilities or expenses arise out of, or are based upon, any such
untrue statement or omission or allegation thereof based upon information
furnished in writing to the Company by the Purchaser or on the Purchaser's
behalf expressly for use therein and; provided, further, that with respect to
                                      --------  -------
any untrue statement or omission or alleged untrue statement or omission made in
any preliminary prospectus, the indemnity agreement contained in this subsection
shall not apply to the extent that any such loss, claim, damage, liability or
expense results from the fact that a current copy of the prospectus was not sent
or given to the person asserting any such loss, claim, damage, liability or
expense at or prior to the written confirmation of the sale of the Registrable
Securities to such person if it is determined that it was the responsibility of
the Purchaser to provide such person with a current copy of the prospectus and
such current copy of the prospectus would have cured the defect giving rise to
such loss, claim, damage, liability or expense.

                                      -5-
<PAGE>

          (b)  Indemnification by Purchaser.  The Purchaser agrees to indemnify
               ----------------------------
and hold harmless, on a joint and several basis, the Company, its directors and
officers and each person, if any, who controls the Company within the meaning of
either Section 15 of the Securities Act or Section 20 of the Exchange Act to the
       ----------
same extent as the foregoing indemnity from the Company to the Purchaser, but
only with respect to information furnished in writing by the Purchaser or on the
Purchaser's behalf expressly for use in the Registration Statement or prospectus
relating to the Registrable Securities, any amendment or supplement thereto or
any preliminary prospectus.  In case any action or proceeding shall be brought
against the Company or its directors or officers, or any such controlling
person, in respect of which indemnity may be sought against the Purchaser, the
Purchaser shall have the rights and duties given to the Company, and the Company
or its directors or officers or such controlling person shall have the rights
and duties given to the Purchaser, by the preceding subsection hereof.

          (c)  Conduct of Indemnification Proceedings.  If any action or
               --------------------------------------
proceeding (including any governmental investigation) shall be brought or
asserted against any person entitled to indemnification under subsections (a) or
(b) above (an "Indemnified Party") in respect of which indemnity may be sought
               -----------------
from any party who has agreed to provide such indemnification (an "Indemnifying
                                                                   ------------
Party"), the Indemnifying Party shall assume the defense thereof, including the
-----
employment of counsel reasonably satisfactory to such Indemnified Party, and
shall assume the payment of all expenses.  Such Indemnified Party shall have the
right to employ separate counsel in any such action and to participate in the
defense thereof, but the fees and expenses of such counsel shall be at the
expense of such Indemnified Party unless (i) the Indemnifying Party has agreed
to pay such fees and expenses or (ii) the named parties to any such action or
proceeding (including any impleaded parties) include both such Indemnified Party
and the Indemnifying Party, and such Indemnified Party shall have been advised
by counsel that there is a conflict of interest on the part of counsel employed
by the Indemnifying Party to represent such Indemnified Party (in which case, if
such Indemnified Party notifies the Indemnifying Party in writing that it elects
to employ separate counsel at the expense of the Indemnifying Party, the
Indemnifying Party shall not have the right to assume the defense of such action
or proceeding on behalf of such Indemnified Party; it being understood, however,
that the Indemnifying Party shall not, in connection with any one such action or
proceeding or separate but substantially similar or related actions or
proceedings in the same jurisdiction arising out of the same general allegations
or circumstances, be liable for the fees and expenses of more than one separate
firm of attorneys (together with appropriate local counsel) at any time for all
such Indemnified Parties, which firm shall be designated in writing by such
Indemnified Parties).  The Indemnifying Party shall not be liable for any
settlement of any such action or proceeding effected without its written
consent, but if settled with its written consent, or if there be a final
judgment for the plaintiff in any such action or proceeding, the Indemnifying
Party shall indemnify and hold harmless such Indemnified Parties from and
against any loss or liability (to the extent stated above) by reason of such
settlement or judgment.

          (d)  Contribution.  If the indemnification provided for in this
               ------------
Section 6 is unavailable to the Indemnified Parties in respect of any losses,
---------
claims, damages, liabilities or judgments referred to herein, then each
Indemnifying Party, in lieu of indemnifying such Indemnified Party, shall
contribute to the amount paid or payable by such Indemnified Party as a result
of such losses, claims, damages, liabilities and judgments in the following
manner: as between

                                      -6-
<PAGE>

the Company on the one hand and each Shareholder on the other, in such
proportion as is appropriate to reflect the relative fault of the Company on the
one hand and each Shareholder on the other in connection with the statements or
omissions which resulted in such losses, claims, damages, liabilities or
judgments, as well as any other relevant equitable considerations.  The relative
fault of the Company on the one hand and of the Purchaser on the other shall be
determined by reference to, among other things, whether the untrue or alleged
untrue statement of a material fact or the omission or alleged omission to state
a material fact relates to information supplied by such party, and the party's
relative intent, knowledge, access to information and opportunity to correct or
prevent such statement or omission.  No person guilty of fraudulent
misrepresentation (within the meaning of subsection 11(f) of the Securities Act)
shall be entitled to contribution from any person who was not guilty of such
fraudulent misrepresentation.

          (e)  Survival.  The indemnity and contribution agreements contained in
               --------
this Section 6 shall remain operative and in full force and effect regardless of
     ---------
(i) any termination of this Agreement, (ii) any investigation made by or on
behalf of any Indemnified Party or by or on behalf of the Company and (iii) the
consummation of the sale or successive resale of the Registrable Securities.

     7.   Miscellaneous.
          -------------

          (a)  Amendments and Waivers.  The provisions of this Agreement may not
               ----------------------
be amended, modified or supplemented, and waivers or consents to departures from
the provisions hereof may not be given other than as initially agreed upon in
writing by the Company and the Purchaser.

          (b)  Notices.  All notices and other communications hereunder shall be
               -------
in writing and shall be deemed given upon (i) transmitter's confirmation of a
receipt of a facsimile transmission, (ii) confirmed delivery by a standard
overnight carrier or when delivered by hand or (iii) the expiration of two
business days after the day when mailed, postage prepaid, addressed at the
following addresses (or at such other address for a party as shall be specified
by like notice):

               (iv)  if to the Purchaser, at the most current address given by
     the Purchaser to the Company, in accordance with the provisions of this
     subsection, which address initially is Guardian Energy Management Corp.,
     2300 Harmon Road, Auburn Hills, Michigan 48326-1714, Attention Vice
     President - Operations, Facsimile No. 248-340-2258, with copy to its
     Secretary, Facsimile No.: 248-340-2175, and thereafter to such other
     address as may be designated from time to time by notice given in
     accordance with the provisions of this Section.

               (v)   if to the Company, initially at 3104 Logan Valley Road,
     Traverse City, Michigan 49685, Attention: Chief Executive Officer,
     Facsimile No.: (231) 941-8312, with a copy of Vinson & Elkins L.L.P., 2001
     Ross Avenue, Suite 3700, Dallas, Texas 75201, Facsimile No.: (214)
     999-7985, Attention: Mark Early, and thereafter at such other address as
     may be designated from time to time by notice given in accordance with the
     provisions of this Section.

                                      -7-
<PAGE>

          (c)  Successors and Assigns.  The Purchaser shall not assign any
               ----------------------
rights or benefits under this Agreement without the prior written consent of the
Company; provided, however, that the Purchaser may assign to any Permitted
Assignee (as that term is defined in the Securities Purchase Agreement) such
rights or benefits without the consent of the Company with respect to Securities
or Conversion Shares transferred to such Permitted Assignee. This Agreement
shall inure to the benefit of and be binding upon the permitted successors and
assigns of the Company and the Purchaser.

          (d)  Counterparts.  This Agreement may be executed in a number of
               ------------
identical counterparts and it shall not be necessary for the Company and the
Purchaser to execute each of such counterparts, but when each has executed and
delivered one or more of such counterparts, the several parts, when taken
together, shall be deemed to constitute one and the same instrument, enforceable
against each in accordance with its terms.  In making proof of this Agreement,
it shall not be necessary to produce or account for more than one such
counterpart executed by the party against whom enforcement of this Agreement is
sought.

          (e)  Headings.  The headings in this Agreement are for convenience of
               --------
reference only and shall not limit or otherwise affect the meaning hereof.

          (f)  Governing Law.  THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED
               -------------
IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, WITHOUT REGARD TO
PRINCIPLES OF CONFLICTS OR CHOICE OF LAW.

          (g)  Severability.  If any provision of this Agreement is held to be
               ------------
illegal, invalid or unenforceable under present or future laws effective during
the term of this Agreement, such provision shall be fully severable; this
Agreement shall be construed and enforced as if such illegal, invalid or
unenforceable provision had never comprised a part of this Agreement; and the
remaining provisions of this Agreement shall remain in full force and effect and
shall not be affected by the illegal, invalid or unenforceable provision or by
its severance from this Agreement.  Furthermore, in lieu of each such illegal,
invalid or unenforceable provision, there shall be added automatically as a part
of this Agreement a provision as similar in terms to such illegal, invalid or
unenforceable provision as may be possible and be legal, valid and enforceable.

          (h)  Entire Agreement.  This Agreement is intended by the Company and
               ----------------
the Purchaser as a final expression of their agreement and is intended to be a
complete and exclusive statement of their agreement and understanding in respect
of the subject matter contained herein. This Agreement supersedes all prior
agreements and understandings between the Company and the Purchaser with respect
to such subject matter.

          (i)  Third Party Beneficiaries.  Other than Indemnified Parties not a
               -------------------------
party hereto, this Agreement is intended for the benefit of the Company and the
Purchaser and their respective successors and permitted assigns and is not for
the benefit of, nor may any provision hereof be enforced by, any other person or
entity other than Permitted Assignees with respect to Securities or Conversion
Shares that the Purchaser has transferred to such Permitted Assignees.

                                      -8-
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date first above written.

                              MILLER EXPLORATION COMPANY

                              By: /s/ Kelly E. Miller
                                 ----------------------------------------------
                              Name: Kelly E. Miller
                                   ---------------------------------------------
                              Title: President
                                    --------------------------------------------

                              GUARDIAN ENERGY MANAGEMENT CORP.

                              By: /s/ Paul A. Halpern
                                 -----------------------------------------------
                              Name: Paul A. Halpern
                                   ---------------------------------------------
                              Title: Vice President - Operations
                                    --------------------------------------------

                                      -9-<PAGE>

                                                                    Exhibit 10.4

                            SUBSCRIPTION AGREEMENT

                          __________________________

     THE SHARES OF COMMON STOCK REFERRED TO HEREIN HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS.  THE
SHARES MAY NOT BE OFFERED FOR SALE, SOLD, PLEDGED, TRANSFERRED, OR OTHERWISE
DISPOSED OF UNTIL THE HOLDER THEREOF PROVIDES EVIDENCE SATISFACTORY TO THE
ISSUER (WHICH, IN THE DISCRETION OF THE ISSUER, MAY INCLUDE AN OPINION OF
COUNSEL SATISFACTORY TO THE ISSUER) THAT SUCH OFFER, SALE, PLEDGE, TRANSFER, OR
OTHER DISPOSITION WILL NOT VIOLATE APPLICABLE FEDERAL OR STATE SECURITIES LAWS.

     This Subscription Agreement (this "Agreement") is made and entered into by
and between Miller Exploration Company, a Delaware corporation (the
"Corporation"), and the undersigned (the "Purchaser") who is subscribing hereby
for 370,370 shares (the "Shares") of the Corporation's common stock, par value
$.01 per share (the "Common Stock").

     In consideration of the Corporation's agreement to sell the Preferred
Shares to the Purchaser, upon the terms and conditions set forth herein, the
Purchaser agrees and represents and warrants to the Corporation as follows:

A.  Subscription.
    ------------

     1.  The Purchaser hereby subscribes for the Shares and for the total dollar
amount (the "Purchase Price") set forth on the signature page below, which
Purchase Price shall be payable in cash by check or by wire transfer (or by such
other form of cash payment as the Corporation desires to accept).

     2.  The Purchaser understands, acknowledges, and agrees that:

         a.  In reliance upon applicable exemptions, the Shares have not been
     registered under the Securities Act of 1933, as amended (the "Securities
     Act"), and the rules and regulations thereunder or any state securities
     laws and the rules and regulations thereunder.

         b.  No federal or state agency has made any finding or determination
     as to the fairness of this Offering for investment or any recommendation or
     endorsement of the Shares.

         c.  Since the Shares have not been registered under the Securities Act
     or applicable state securities laws, the economic risk of the investment
     must be borne

                                       1
<PAGE>

     indefinitely by the Purchaser, and the Shares cannot be sold,
     pledged, hypothecated, or otherwise transferred unless subsequently
     registered under the Securities Act and such laws, or an exemption from
     such registration is available, and there is compliance with the
     requirements of this Agreement; such registration under the Securities Act
     and such laws is unlikely at any time in the future; and the Corporation is
     not obligated to file a notification under Regulation A of the Securities
     Act or a registration statement under the Securities Act or any state
     securities laws.

         d.  No assignment, sale, pledge, hypothecation, transfer, exchange, or
     other disposition, or offer, of the Shares can be made without the prior
     written approval of the Corporation.  No transfer will be permitted by the
     Corporation, which, in the view of the Corporation, would jeopardize the
     Corporation's compliance with federal or state securities laws.

         e.  The Shares are speculative investments which involve a high degree
     of risk of loss by the Purchaser.

         f.  Due to the high degree of risk of loss, Shares only may be sold to
     persons who understand the nature of the Corporation and who are
     "Accredited Investors" (as defined in Rule 501(a) of Regulation D
     promulgated under the Securities Act).

B.   Representations, Warranties, and Agreements.
     -------------------------------------------

     1.  The Purchaser hereby represents, warrants, and agrees that:

         a.  The Purchaser is acquiring the Shares for his own account for
     investment, and not with a view to distribution, resale, subdivision, or
     fractionalization thereof; and the undersigned has no present plans to
     enter into any contract, undertaking, agreement, or arrangement for
     distribution, resale, subdivision, or fractionalization of any of the
     Shares.  In order to induce the Corporation to issue and sell the Shares
     subscribed for hereby to the undersigned, it is agreed that the Corporation
     will have no obligation to recognize the ownership, beneficial or
     otherwise, of the Shares comprising such Shares by anyone but the
     undersigned.

         b.  (i) The Purchaser can bear the economic risk of losing his entire
     investment; (ii) his overall commitment to investments which are not
     readily marketable is not disproportionate to his net worth, and his
     investment in the Shares will not cause such overall commitment to become
     excessive; (iii) he has adequate means of providing for his current needs
     and personal contingencies and has no need for liquidity in his investment
     in the Shares; and (iv) he has such knowledge and experience in financial
     and business matters that he is capable of evaluating the risks and merits
     of this investment.

                                       2
<PAGE>

        c.  The Purchaser has carefully read or reviewed and is familiar with
     the Corporation's (i) Annual Report on Form 10-K for the year ended
     December 31, 1999 (the "10-K") and (ii) Quarterly Report on Form 10-Q for
     the three months ended March 31, 2000.  The Corporation has made available
     to the Purchaser and/or his attorney and/or his accountant all agreements,
     documents, records, and books that he or they have requested relating to an
     investment in the Corporation.  The Purchaser and/or his attorney and/or
     his accountant all have had an opportunity to ask questions of and receive
     answers from the Corporation, or a person or persons acting on its behalf,
     concerning the terms and conditions of this investment, and answers have
     been provided to all of his or their questions concerning an investment in
     the Corporation.  In evaluating the suitability of an investment in the
     Corporation, the Purchaser has not been furnished and has not relied upon
     any representations or other information (whether oral or written) other
     than as contained in any documents, information, or answers to questions so
     furnished to him by the Corporation.

         d.  The Purchaser recognizes that investment in the Corporation
     involves certain risks, and he has taken full cognizance of and understands
     all of the risk factors related to the purchase of the Shares, including,
     but not limited to, those set forth under the caption "Risk Factors" in the
     10-K.

         e.  The Purchaser has discussed with his professional legal, tax, and
     financial advisors the suitability of the investment in the Corporation for
     his particular tax and financial situation.  All information which the
     Purchaser has provided to the Corporation concerning himself and his
     financial position is correct and complete as of the date set forth below,
     and, if there should be any material change in such information prior to
     the acceptance of the Purchaser's subscription and the sale of the Shares,
     he will immediately provide such information to the Corporation.

         f.  If this Agreement is executed and delivered on behalf of a
     partnership, corporation, trust, pension plan, estate, or other entity, (i)
     the person signing this Agreement on behalf of such entity has been duly
     authorized to execute and deliver this Agreement and all other instruments
     executed and delivered on behalf of such partnership, corporation, trust,
     pension plan, estate, or other entity in connection with the purchase of
     the Shares; (ii) the signature of the person signing this Agreement is
     binding upon such partnership, corporation, trust, pension plan, estate, or
     other entity; and (iii) the Purchaser was not organized for the specific
     purpose of acquiring the Shares.

         g.  The address set forth below is the Purchaser's true and correct
     residence or principal place of business, and the Purchaser has no present
     intention of becoming a resident of any other state or jurisdiction or
     moving its principal place of business.

         h.  The undersigned Purchaser is an "Accredited Investor" (as defined
     in Rule 501(a) of Regulation D promulgated under the Securities Act).

                                       3
<PAGE>

         i.  The undersigned understands and agrees, and acknowledges that it
     has been disclosed to him, that the following restrictions and limitations
     are applicable to the undersigned's purchase and resales, pledges,
     hypothecations, or other transfers of the Shares, and, therefore, that the
     undersigned must bear the economic risk of investment in the Shares for an
     indefinite period of time as described in subparagraph A. 4. h.:

          (i)    The Shares have not been registered, as described in
          subparagraph A. 4. f. above and, therefore, cannot be sold, pledged,
          hypothecated, or otherwise transferred unless they are registered
          under the Securities Act and applicable state securities laws, or an
          exemption from such registration is available.

          (ii)   A legend has been placed on the certificates representing the
          Shares in substantially the following form:

                 THE SHARES OF STOCK REPRESENTED BY THIS CERTIFICATE HAVE NOT
                 BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED,
                 OR ANY STATE SECURITIES LAWS. THE SHARES MAY NOT BE OFFERED FOR
                 SALE, SOLD, PLEDGED, TRANSFERRED, OR OTHERWISE DISPOSED OF
                 UNTIL THE HOLDER HEREOF PROVIDES EVIDENCE SATISFACTORY TO THE
                 ISSUER (WHICH, IN THE DISCRETION OF THE ISSUER, MAY INCLUDE AN
                 OPINION OF COUNSEL SATISFACTORY TO THE ISSUER) THAT SUCH OFFER,
                 SALE, PLEDGE, TRANSFER, OR OTHER DISPOSITION WILL NOT VIOLATE
                 APPLICABLE FEDERAL OR STATE SECURITIES LAWS.

          (iii)  Stop transfer instructions have been or will be placed with
          respect to the Shares so as to restrict the resale, pledge,
          hypothecation, or other transfer thereof.

          (iv)   The legend and stop transfer instructions described in
          subparagraphs (ii) and (iii) above will be placed with respect to any
          new certificate issued upon presentment by the undersigned of a
          certificate for transfer for so long as such legend and instructions
          are deemed advisable by the Corporation.

          j.    It has never been represented, guaranteed or warranted to the
     undersigned by the Corporation, its agents or employees, or any other
     person, expressly or by implication, any of the following:

          (i)   The appropriate or exact length of time that the undersigned
          will be required to remain as owner of the undersigned's Shares.

                    OR
                    --

                                       4
<PAGE>

          (ii)   The percentage of profit and/or amount or type of
          consideration, profit, or loss (including tax writeoffs and/or tax
          benefits) to be realized, if any, as a result of this investment.

          k.     If the undersigned Purchaser is an individual, initial below:

-----                 (i)   The net worth (i. e., total assets minus total
Initial if         liabilities) at the date hereof of the undersigned, or joint
Applicable         net worth with the undersigned's spouse, exceeds $ 1,000,000.

                                OR
                                --

-----                 (ii)  The undersigned had individual income (not including
Initial if          spouse's income) in excess of $200,000 in each of the two
Applicable          most recent years or joint income with spouse in excess of
                    $300,000 in each of those years and reasonably expects to
                    reach the same income level in the current year.

     The undersigned's United States social security number is ---_____________.

          l.  If the undersigned Purchaser is an entity, initial below:

-----                 (i)  Each of the equity owners of the undersigned is an
Initial if          individual and satisfies at least one of the tests set forth
Applicable          in subparagraphs (k)(i) or (k)(ii) above.  (If this item has
                    been initialed, have each of such equity owners execute and
                    furnish a Certificate of Financial Position in the form of
                    Schedule 1 hereto).

                    OR
                    --

                                       5
<PAGE>

-----                (ii)  The entity is an organization described in section
Initial if         501(C)(3) of the Internal Revenue Code of 1986, as amended,
Applicable         corporation, a Massachusetts or similar business trust, or a
                   partnership, not formed for the specific purpose of acquiring
                   the Shares, with total assets in excess of $5,000,000.

     The undersigned's United States employer identification number is
____________________.  The undersigned's place of incorporation or organization
is ___________________.

     2.  The foregoing representations and warranties are true and accurate as
of the date hereof and shall be true and accurate as of the date of the
acceptance hereof by the Corporation and the sale of the Shares to the
Purchaser.  If in any respect such representations and warranties shall not be
true and accurate prior thereto, the Purchaser will give written notice of such
fact to the Corporation specifying which representations and warranties are not
true and accurate and the reasons therefor.

C.   Miscellaneous.
     -------------

     1.  All pronouns and any variations thereof used herein shall be deemed to
refer to the masculine, feminine, neuter, singular, or plural as the identity of
the person or persons may require.

     2.  Notices required or permitted to be given hereunder shall be in writing
and shall be deemed to be sufficiently given when personally delivered or when
sent by registered or certified mail, return receipt requested, (i) if to the
Purchaser, at the address set forth on the signature page hereof, and (ii) if to
the Corporation, at 3104 Logan Valley Road, Traverse City, Michigan 49685, as
either of such addresses may be changed from time to time by notice given in
accordance with this paragraph.

     3.  Failure of the Corporation to exercise any right or remedy under this
Agreement or any other agreement between the Corporation and the Purchaser, or
otherwise, or delay by the Corporation in exercising same, will not operate as a
waiver thereof.  No waiver by the Corporation will be effective unless and until
it is in writing and signed by the Corporation.

     4.  This Agreement shall be enforced, governed, and construed in all
respects in accordance with the laws of the State of Delaware.  This Agreement
and the rights, powers, and duties set forth herein shall be binding upon the
Purchaser, his heirs, estate, legal representatives, successors, and assigns and
shall inure to the benefit of the Corporation, its successors, and assigns.  In
the event that any

                                       6
<PAGE>

provision of this Agreement is invalid or unenforceable under
any applicable statute or rule of law, then such provision shall be deemed
inoperative to the extent that it may conflict therewith and shall be deemed
modified to conform with such statute or rule of law.  Any provision hereof
which may prove invalid or unenforceable under any law shall not affect the
validity or enforceability of any other provision hereof.

     5.  This Agreement constitutes the entire agreement between the parties
hereto with respect to the subject matter hereof and may be amended only by a
writing executed by all parties.

                                       7
<PAGE>

                               _________________
                            Subscription Agreement
                                SIGNATURE PAGE

     IN WITNESS WHEREOF, the Purchaser has executed this Agreement as of the
11th day of July, 2000.

  Number of Preferred Shares               Ecco Investments, L.L.C.
  subscribed for at                        ------------------------------------
  $1.35 per Share:                         Print name(s) of Purchaser(s)

                                           ------------------------------------
  370,370

  Total Purchase Price:                    By:
                                                -------------------------------
                                                        Signature(s) of

  $499,999.50                              ------------------------------------
                                           ------------------------------------
                                           Robert M. Boeve, Member
                                           ------------------------------------
                                           Print title of person signing, if
                                           signing as an authorized
                                           representative of Purchaser

Make check payable to the order of:        Address of Purchaser's residence or
Miller Exploration Company                 principal place of business (Please
                                           print or type):

                                           ------------------------------------
                                           ------------------------------------
                                           ------------------------------------

   ___  Individual Ownership                              ___  Trust
   ___  Separate Property                                 ___  Corporation
   ___  Community Property                                ___  Pension Plan
   ___  Joint Tenancy(1)                                  ___  Estate
   ___  Tenancy in Common(1)(2)                            X   Other (please
                                                          ___
                                                          indicate  L.L.C.
                                                                    ______
----------------------

(1) Each person involved is be required to be an "Accredited Investor."
(2)  Both husband and wife must sign.
------------------------------------------------------

                                       8
<PAGE>

Subscription for 370,370 Shares at $1.35 per Share, for a total of $499,999.50,
accepted as of July 11, 2000.

                         MILLER EXPLORATION COMPANY

                         By:  _______________________
                         Name:_______________________
                         Title:______________________

                                       9
<PAGE>

                               INDIVIDUAL, JOINT
                           OR PARTNER ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  The undersigned Notary Public does hereby certify that on this _____ day of
_______________, 2000, personally appeared _________________________* known to
me to be the person whose name is subscribed to the foregoing instrument, who,
being by me duly sworn, declared and acknowledged to me that the same was his
free act and deed and that he executed and delivered same for the purposes and
consideration therein expressed and in the capacity therein stated, and that the
statements therein contained are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert name of individual or joint tenant or partner executing on behalf of
partnership.

            ACKNOWLEDGMENT BY HUSBAND AND WIFE AS TENANTS IN COMMON

STATE OF _______________________

COUNTY OF ______________________

  The undersigned Notary Public does hereby certify that on this _____ day of
________________, 2000, personally appeared __________________________ and
_________________________* known to me to be the persons whose names are
subscribed to the foregoing instrument, who, being by me duly sworn, declared
and acknowledged to me that the same were their free acts and deeds and that
they executed and delivered such instrument for the purposes and consideration
therein expressed and in the capacity therein stated, and that the statements
contained therein are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert names of husband and wife.

                                       10
<PAGE>

                   LIMITED LIABILITY COMPANY ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  On this 11th day of July, 2000, before me appeared Robert M. Boeve to me
personally known, who, being by me duly sworn, declared and acknowledged to me
that he is a member of Ecco Investments, L.L.C. and that the foregoing
instrument was executed and delivered on behalf of said limited liability
company by authority of the members and said Robert M. Boeve acknowledged said
instrument to be the free act and deed of said limited liability company, and
that the statements therein contained are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------

                 TRUST, PENSION PLAN, OR ESTATE ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  On this _____ day of ________________, 2000, before me appeared
__________________________* to me personally known, who, being by me duly sworn,
declared and acknowledged to me that he is the Trustee, Administrator, or
Executor of the _________________________** and that the foregoing instrument
was executed and delivered on behalf of said Trust, Pension Plan, or Estate by
authority of its Trustee, Administrator, or Executor and said
__________________________* acknowledged said instrument to be the free act and
deed of said Trust, Pension Plan, or Estate, and that the statements therein
contained are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert name of Trustee, Administrator, or Executor.
**  Insert name of Trust, Pension Plan, or Estate.

                                       11
<PAGE>

                                  SCHEDULE 1

                       CERTIFICATE OF FINANCIAL POSITION

  This Certificate of Financial Position is provided by the undersigned pursuant
to subparagraph B.1.1.(i) of the Subscription Agreement (the "Subscription
Agreement") executed by the Purchaser named below relating to a subscription for
Miller Exploration Company, a Delaware corporation (the "Corporation").

  The undersigned represents and warrants to the Corporation that:

-----            (i)  The net worth (i.e., total assets minus total liabilities)
Initial if     at the date hereof of the undersigned, or joint net worth with
Applicable     the undersigned's spouse, exceeds $1,000,000.  The undersigned
               undertakes to inform the Corporation immediately if such net
               worth is less than $1,000,000 prior to the acceptance by the
               Corporation of the Purchaser's subscription.

               OR
               --

-----            (ii)  The undersigned had individual income (not including
Initial if     spouse's income) in excess of $200,000 in each of the two most
Applicable     recent years or joint income with spouse in excess of $300,000
               in each of those years and reasonably expects to reach the same
               income level in the current year.  The undersigned undertakes
               to inform the Corporation immediately if this representation
               and warranty becomes untrue prior to the acceptance by the
               Corporation of the Purchaser's subscription.

Dated:
-----
               -------------------------------
               (Signature)

               Name:
                      ------------------------
                      (Please Print)

               -------------------------------
               Relationship to Purchaser

               -------------------------------
               Name of Purchaser

                                       12

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