FALCON FUND LTD
SC 13G, 1998-08-28
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<PAGE>   1
                                                                           
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13G
                                 (RULE 13d-102)

           INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT
         TO RULES 13d-1(c) AND AMENDMENTS FILED PURSUANT TO 13d-2(b)


                           MILLER EXPLORATION COMPANY
- --------------------------------------------------------------------------------
                                (Name of Issuer)

                    Common Stock,  $0.01 Par Value Per Share
- --------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                  600533-10-3
                    -----------------------------------------
                                 (CUSIP Number)


                                August 21, 1998
          -----------------------------------------------------------
            (Date of Event which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

                    [ ]  Rule 13d-1(b)
                    [X]  Rule 13d-1(c)
                    [ ]  Rule 13d-1(d)



<PAGE>   2
                                  SCHEDULE 13G

CUSIP NO. 600533-10-3
- --------------------------------------------------------------------------------
1     NAME OF REPORTING PERSON
      S.S. OR IRS. IDENTIFICATION NO. OF ABOVE PERSON

      Falcon Fund, Ltd.
      75-2345424

- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP                  (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     CITIZENSHIP OR PLACE OF ORGANIZATION

                Texas
- --------------------------------------------------------------------------------
                  5     SOLE VOTING POWER              None 
   NUMBER OF
    SHARES          
 BENEFICIALLY     --------------------------------------------------------------
   OWNED BY       6     SHARED VOTING POWER            649,600
     EACH     
   REPORTING            
    PERSON        --------------------------------------------------------------
     WITH         7     SOLE DISPOSITIVE POWER         None     
              
                    
                  --------------------------------------------------------------
                  8     SHARED DISPOSITIVE POWER       649,600

                    
- --------------------------------------------------------------------------------
9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON      649,600


- --------------------------------------------------------------------------------
10    CHECK BOX IF THAT AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES [ ]
                                                                            
- --------------------------------------------------------------------------------
11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)                 5.2%

- --------------------------------------------------------------------------------
12    TYPE OF REPORTING PERSON                                          PN

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



<PAGE>   3
                                  SCHEDULE 13G

CUSIP NO. 600533-10-3
- --------------------------------------------------------------------------------
1     NAME OF REPORTING PERSON
      S.S. OR IRS. IDENTIFICATION NO. OF ABOVE PERSON

      G. Houston Hall
      ###-##-####

- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP                  (a) [ ]
                                                                        (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     CITIZENSHIP OR PLACE OF ORGANIZATION

                USA
- --------------------------------------------------------------------------------
                  5     SOLE VOTING POWER             None
   NUMBER OF
    SHARES          
 BENEFICIALLY     --------------------------------------------------------------
   OWNED BY       6     SHARED VOTING POWER           649,600 (1)
     EACH     
   REPORTING        
    PERSON    
     WITH         --------------------------------------------------------------
                  7     SOLE DISPOSITIVE POWER        None
            
                     
                  --------------------------------------------------------------
                  8     SHARED DISPOSITIVE POWER      649,600 (1)

                    
- --------------------------------------------------------------------------------
9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

             649,600 (1)
- --------------------------------------------------------------------------------
10    CHECK BOX IF THAT AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES [ ]
                                                                            
- --------------------------------------------------------------------------------
11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      5.2%
- --------------------------------------------------------------------------------
12    TYPE OF REPORTING PERSON

              IN
- --------------------------------------------------------------------------------

(1)      Mr. Hall, as General Partner of Falcon Fund, Ltd., has voting and
         dispositive power with respect to the aggregate 649,600 shares of
         Common Stock held by Falcon Fund, Ltd.
<PAGE>   4
CUSIP NO. 600533-10-3               13 G 



ITEM 1(a).      NAME OF ISSUER: 

                Miller Exploration Company

ITEM 1(b).      ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

                3104 Logan Valley Road
                Traverse City, Michigan 49685-0348


ITEM 2(a).      NAME OF PERSON FILING:

                Falcon Fund, Ltd.,                G. Houston Hall
                a Texas limited partnership

ITEM 2(b).      ADDRESS OF PRINCIPAL BUSINESS OFFICE OR, IF NONE, RESIDENCE:

                8235 Douglas Avenue, Suite 420, Dallas, Texas 75225

ITEM 2(c).      CITIZENSHIP:

                United States

ITEM 2(d).      TITLE OF CLASS OF SECURITIES:

                Common Stock, $.01 par value

ITEM 2(e).      CUSIP NUMBER:

                600533-10-3

ITEM 3.         If this statement is filed pursuant to Rule 13d-1(c) or 13d-
                2(b) or (c), check whether the person filing is a:

                (a) through (j) are not applicable

                If this statement is filed pursuant to Rule 13d-1(c), check
                this box [X]
<PAGE>   5
CUSIP NO. 600533-10-3               13 G


         
ITEM 4.          OWNERSHIP

         Provide the following information regarding the aggregate number and
         percentage of the class of securities of the issuer identified in Item
         1.

         (a) Amount beneficially owned:

                  649,600 shares

         (b) Percent of Class:

                  5.2%

         (c) Number of shares as to which such person has:
             
             (i)   Sole power to vote or to direct the vote: None.
             (ii)  Shared power to vote or to direct the vote: 649,600 (1)
             (iii) Sole power to dispose or to direct the disposition of: None.
             (iv)  Shared power to dispose or to direct the disposition of:
                   649,600 (1)

ITEM 5.  OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

         If this statement is being filed to report the fact that as of the
         date hereof the reporting person has ceased to be the beneficial owner
         of more than five percent of the class of securities, check the
         following [ ].

ITEM 6.  OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.

         Mr. Hall, as general partner of Falcon Fund, Ltd., has the power to
         direct the receipt of dividends from, or the proceeds from the sale of,
         the Common Stock held by Falcon Fund, Ltd. reported herein in the
         manner prescribed by the partnership agreement of Falcon Fund, Ltd.

ITEM 7.  IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH ACQUIRED THE
         SECURITY BEING REPORTED ON BY THE PARENT HOLDING COMPANY. 

         Not applicable.

ITEM 8.  IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP.

         Not applicable.

ITEM 9.  NOTICE OF DISSOLUTION OF GROUP. 

         Not applicable.

ITEM 10. CERTIFICATION.

         By signing below I certify that, to the best of my knowledge and
         belief, the securities referred to above were not acquired and are not
         held for the purpose of or with the effect of changing or influencing
         the control of the issuer of the securities and were not acquired and
         are not held in connection with or as a participant in any transaction
         having that purpose or effect.

Exhibits:

        The following is filed as an exhibit to this Statement on Schedule 13 G:

        Exhibit A         Agreement to File Statement

- ----------------------
(1)  Mr. Hall, as General Partner of Falcon Fund, Ltd., has voting and
     dispositive power with respect to the aggregate 649,600 shares of Common
     Stock held by Falcon Fund, Ltd.
<PAGE>   6

CUSIP NO. 600533-10-3               13 G                     




         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


Dated as of August 27, 1998              Falcon Fund, Ltd.

                                         By: /s/  G. Houston Hall            
                                             --------------------------------
                                             General Partner


                                         /s/ G. Houston Hall                 
                                         ------------------------------------
                                         G. Houston Hall
<PAGE>   7

                                                                       EXHIBIT A

                          Agreement to File Statement

     The undersigned hereby agree to file Schedule 13 G on behalf of each of
them relating to purchases of the common stock of Miller Exploration Company by 
Falcon Fund, Ltd.

                                                  Falcon Fund, Ltd.


                                                  By:   /s/ G. HOUSTON HALL
                                                      -------------------------
                                                            General Partner


                                                      /s/ G. HOUSTON HALL
                                                      -------------------------
                                                            G. Houston Hall


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