Document:

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                                                                     Exhibit 4.3

                           MILLER EXPLORATION COMPANY

                             AMENDMENT NO. 2 TO THE
                   MILLER EXPLORATION COMPANY STOCK OPTION AND
                          RESTRICTED STOCK PLAN OF 1997

     This Amendment No. 2 to the Miller Exploration Company Stock Option and
Restricted Stock Plan of 1997 (this "Amendment") is made and adopted by Miller
Exploration Company, a Delaware corporation (the "Company"), effective as of
_________, 2001.

                                    RECITALS

     WHEREAS, the Board of Directors and Shareholders of the Company have duly
approved this Amendment to amend the terms and provisions of the Miller
Exploration Company Stock Option and Restricted Stock Plan of 1997, as amended
(the "Plan"); and

     WHEREAS, any capitalized term used and not otherwise defined herein shall
have the meaning set forth in the Plan.

                                    AMENDMENT

          1. The Plan is hereby amended by deleting Section 4.1 thereof in its
     entirety and substituting in lieu thereof the following:

               4.1 NUMBER OF SHARES. Subject to adjustment as provided in
          Section 4.3 of the Plan, a maximum of 2,400,000 shares of Common Stock
          shall be available for Incentive Awards under the Plan. Such Shares
          may be authorized but unissued shares.

          2. Except as expressly set forth herein, the Plan shall remain in full
     force and effect without further amendment or modification.

                            [SIGNATURE PAGE FOLLOWS]
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     IN WITNESS WHEREOF, the Company, acting by and through its officer hereunto
duly authorized, has executed this Amendment effective as of the date first
written above.

                                          MILLER EXPLORATION COMPANY

                                          By:
                                              ---------------------------------
                                          Name:  Deanna L. Cannon
                                          Title: Vice President - Finance
                                                 and Secretary<PAGE>

                                                                     Exhibit 4.5
                           MILLER EXPLORATION COMPANY

    AMENDED AND RESTATED EQUITY COMPENSATION PLAN FOR NON-EMPLOYEE DIRECTORS

                                   SECTION 1

                       Establishment and Purpose of Plan
                       ------------- --- ------- -- ----

     The Company hereby establishes the Equity Compensation Plan for Non-
Employee Directors (the "Plan") for its non-employee directors.  The purposes of
the Plan are to provide an opportunity and means by which non-employee directors
can increase their financial interest in the Company, and thereby increase their
personal interest in the Company's continued success, through the payment of
directors' fees in Company Common Stock.

                                   SECTION 2

                                  Definitions
                                  -----------

     The following words have the following meanings unless a different meaning
is plainly required by the context:

     2.1  "Award" means the award of Common Stock to a Participant under the
Plan.

     2.2  "Committee" means a committee designated by the Board of Directors of
the Company to administer the Plan or, if no committee is designated, the Board
of Directors.

     2.3  "Common Stock" means the Common Stock of the Company, $.01 par value.

     2.4  "Company" means Miller Exploration Company, a Delaware corporation,
and its subsidiaries.

     2.5  "Director's Fee" means the amount of income payable to a Participant
for service as a director for a fiscal year, including without limitation
payments for attendance at meetings of the Board of Directors or meetings of
committees of the Board of Directors, and any retainer fee paid to members of
the Board of Directors, but excluding reimbursement of costs.
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     2.6  "Market Value" of any security on any given date means if the security
is listed for trading on The Nasdaq Stock Market or one or more national
securities exchanges, the last reported sales price on the date in question, or
if such security shall not have been traded on such principal exchange on such
date, the last reported sales price on the first day prior thereto on which such
security was so traded.

     2.7  "Non-Employee Director" shall mean a director of the Company who is
not employed by the Company or its subsidiaries.

     2.8  "Participant" means the Non-Employee Directors of the Company who are
granted Awards under the Plan.

                                   SECTION 3

                                 Administration
                                 --------------

     3.1  Power and Authority.  The Committee shall administer the Plan.  Except
as limited in this Plan, the Committee shall have full power and authority to
interpret the provisions of the Plan and Awards granted under the Plan, to
supervise the administration of the Plan and Awards granted under the Plan and
to make all other determinations considered necessary or advisable under the
Plan.  All determinations, interpretations, and selections made by the Committee
regarding the Plan shall be final and conclusive.  The Committee may delegate
recordkeeping, calculation, payment, and other ministerial administrative
functions to individuals designated by the Committee, who may be employees of
the Company.

     3.2  Awards to Participants.  In accordance with and subject to the
provisions of the Plan, the Committee shall have the authority to grant Awards
under the Plan

     3.3  Indemnification of Committee Members.  Neither any member or former
member of the Committee nor any individual to whom authority is or has been
delegated shall be personally responsible or liable for any act or omission in
connection with the performance of powers or duties or the exercise of
discretion or judgment in the administration and implementation of the Plan.
Each person who is or shall have been a member of the Committee shall be
indemnified and held harmless by the Company from and against any cost,
liability, or expense imposed or incurred in connection with such person's or
the Committee's taking or failing to take any action under the Plan.  Each such
person shall be justified in relying on information furnished in connection with
the Plan's administration by any appropriate person or persons.

                                      -2-
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                                   SECTION 4

                           Shares Subject to the Plan
                           ------ ------- -- --- ----

     4.1  Number of Shares.  Subject to adjustment as provided in Section 4.2, a
maximum of 320,000 shares of Common Stock shall be available for Awards under
the Plan.  Such shares may be authorized but unissued shares.

     4.2  Adjustments.  If the number of shares of Common Stock outstanding
changes by reason of a stock dividend, stock split, recapitalization, merger,
consolidation, combination, exchange of shares, or any other change in the
corporate structure or shares of the Company, the aggregate number and class of
shares available for Awards under the Plan shall be appropriately adjusted.  No
fractional shares shall be issued pursuant to the Plan, and any fractional
shares resulting from adjustments shall be eliminated from the respective Award,
with an appropriate cash adjustment for the value of any Awards eliminated.

                                   SECTION 5

                                    Awards
                                    ------

     5.1  Grant. In accordance with the provisions of Section 5.3, Each Non-
Employee Director shall receive an Award in respect of any Director's Fee that
would otherwise be payable to such Non-Employee Director.

     5.2  Determination of Number of Shares.  The number of shares of Common
Stock (rounded to the nearest whole share) to be awarded to a Participant shall
be calculated by dividing the dollar amount of a Participant's Director's Fee
for a fiscal year by the Market Value of the Common Stock on the day before the
payment date.

     5.3  Time of Payment by the Company.  The Company shall distribute or cause
to be distributed to a Participant the number of shares of Common Stock as
calculated in Section 5.2 on or before the 45th day after the end of the
Company's fiscal year in which the Director's Fees are earned. The time of
payment may be amended before or after an Award (a) by the Committee in its sole
discretion, if the terms of such amendment benefits the Participant, or (b) in
all other cases, by the Committee with the consent of the Participant.

                                      -3-
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                                   SECTION 6

                               General Provisions
                               ------- ----------

     6.1  No Rights to Awards.  No Participant or other person shall have any
claim to be granted any Award, and there is no obligation of uniformity of
treatment of Participants.  The terms and conditions of the Awards of the same
type and the determination of the Committee to grant a waiver or modification of
any Award and the terms and conditions thereof need not be the same with respect
to each Participant.

     6.2  Compliance With Laws; Listing and Registration of Shares.  All
issuances of Common Stock under the Plan shall be subject to applicable laws,
rules, and regulations, and to the requirement that if at any time the Committee
determines, in its sole discretion, that the listing, registration, or
qualification of the shares covered thereby upon any securities exchange or
under any state or federal law, or the consent or approval of any governmental
regulatory body, is necessary or desirable as a condition of, or in connection
with, the issue of shares thereunder, such Award may not be granted in whole or
in part, unless and until such listing, registration, qualification, consent, or
approval shall have been effected or obtained free of any conditions not
acceptable to the Committee.

     6.3  No Limit on Other Compensation Arrangements.  Nothing contained in the
Plan shall prevent the Company from adopting or continuing in effect other or
additional compensation arrangements, including the grant of options and other
stock-based awards, and such arrangements may be either generally applicable or
applicable only in specific cases.

     6.4  No Right to Directorship.  The grant of an Award shall not be
construed as giving a Participant the right to be retained in the directorship
of the Company.

     6.5  Governing Law.  The validity, construction, and effect of the Plan and
any rules and regulations relating to the Plan shall be determined in accordance
with the laws of the State of Delaware and applicable federal law.

     6.6  Severability.  In the event any provision of the Plan shall be held
illegal or invalid for any reason, the illegality or invalidity shall not affect
the remaining parts of the Plan, and the Plan shall be construed and enforced as
if the illegal or invalid provision had not been included.

     6.7  Unfunded Plan.  This Plan shall be an unfunded plan within the meaning
of the Internal Revenue Code of 1986, as amended.  Benefits provided in the Plan
constitute only an unsecured contractual promise to pay in accordance with the
terms of the Plan by the Company.

                                      -4-
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                                   SECTION 7

                    Effective Date and Duration of the Plan
                    --------- ---- --- -------- -- --- ----

     This Plan shall take effect December 7, 1998, which is the effective date
of approval by the Board of Directors. This Plan as initially adopted was
approved by the stockholders of the Company on June 11, 1999. An amended and
restated Plan was approved by the Board of Directors on February 25, 2000 and
approved by the stockholders of the Company on May 26, 2000. Unless earlier
terminated by the Board of Directors, no Award shall be granted under this Plan
after December 6, 2008.

                                   SECTION 8

                           Termination and Amendment
                           ----------- --- ---------

     The Board may terminate the Plan at any time, or may from time to time
amend the Plan, provided that no such amendment may impair any outstanding Award
without the consent of the Participant.  No termination, amendment, or
modification of the Plan shall become effective with respect to any Award
previously granted under the Plan without the prior written consent of the
Participant holding such Award unless such amendment or modification benefits
the Participant.

                                      -5-

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