Exhibit 3.1(b)
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                            CERTIFICATE OF AMENDMENT
                                       TO
                          CERTIFICATE OF INCORPORATION
                                       OF
                           MILLER EXPLORATION COMPANY

               Pursuant to Section 242 of the General Corporation
                          Law of the State of Delaware

     Miller Exploration Company, a corporation organized and existing under and
by virtue of the General Corporation Law of the State of Delaware (the
"Corporation"), hereby certifies:

     FIRST, that the board of directors of the Corporation duly adopted
resolutions proposing and declaring advisable the following amendment to the
Certificate of Incorporation of the Corporation in accordance with the
provisions of Section 242 of the General Corporation Law of the State of
Delaware and directing that such amendment be submitted to the stockholders of
the Corporation for their approval:

     "RESOLVED, that the Board of Directors of the Corporation deems and
declares advisable and approves an amendment to the Certificate of Incorporation
of the Corporation to amend the first paragraph of Article IV to read in its
entirety as follows:

     The total authorized capital stock of the corporation is 40 million
(40,000,000) shares of common stock, $.01 per value per share, and 2 million
(2,000,000) shares of preferred stock, $.01 par value per share.

     SECOND, that the previously stated amendment to the Certificate of
Incorporation of the Corporation was duly adopted by the stockholders of the
Corporation in accordance with the provisions of Section 242 and of the General
Corporation Law of the State of Delaware.

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     IN WITNESS WHEREOF, the undersigned has executed this Certificate this 25th
day of June, 1999.

                              MILLER EXPLORATION COMPANY



                              By:     /s/ Wm. J. Bumgartner
                                      ------------------------------
                              Name:   Wm. J. Bumgartner
                                      ------------------------------
                              Title:  VP Finance
                                      ----------------------------

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