UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13G

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                              (AMENDMENT NO. __ )*


                          BRONCO DRILLING COMPANY, INC.
                          -----------------------------
                                (Name of Issuer)

                                  Common Stock
                                  ------------
                         (Title of Class of Securities)

                                    112211107
                                    ---------

                                 (CUSIP Number)


                                December 31, 2005
                                -----------------
             (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)
     /__/    Rule 13d-1(c)
     /X/     Rule 13d-1(d)


*    The remainder of this cover page shall be filled out for a reporting
     person's initial filing on this form with respect to the subject class of
     securities, and for any subsequent amendment containing information which
     would alter disclosures provided in a prior cover page.

     The information required on the remainder of this cover page shall not be
     deemed to be "filed" for the purpose of Section 18 of the Securities
     Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of
     that section of the Act but shall be subject to all other provisions of the
     Act (however, see the Notes).


                                  Page 1 of 10



CUSIP N. 112211107


--------------------------------------------------------------------------------
1)   Names of Reporting Person.                              WEXFORD CAPITAL LLC
     I.R.S. Identification Nos. of Above Person (entities only)
--------------------------------------------------------------------------------

2)   Check the Appropriate Box if a Member of a Group                    (a) [ ]
     (See Instructions)                                                  (b) [ ]
--------------------------------------------------------------------------------

3)   SEC Use Only
--------------------------------------------------------------------------------

4)   Citizenship or Place of Organization                            Connecticut
--------------------------------------------------------------------------------
                        5)  Sole Voting Power                                  0
     Number of Shares   --------------------------------------------------------
     Beneficially       6)  Shared Voting Power                       13,092,353
     Owned by Each      --------------------------------------------------------
     Reporting          7)  Sole Dispositive Power                             0
     Person With        --------------------------------------------------------
                        8)  Shared Dispositive Power                  13,092,353
--------------------------------------------------------------------------------

9)   Aggregate Amount Beneficially Owned by Each Reporting Person     13,092,353
--------------------------------------------------------------------------------

10)  Check if the Aggregate Amount in Row (9) Excludes
     Certain Shares (See Instructions)                                       [ ]
--------------------------------------------------------------------------------

11)  Percent of Class Represented by Amount in Row 9                      56.52%
--------------------------------------------------------------------------------

12)  Type of Reporting Person (See Instructions)                              OO
--------------------------------------------------------------------------------


                                  Page 2 of 10



CUSIP N. 112211107


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

1)   Names of Reporting Person.                 BRONCO DRILLING HOLDINGS, L.L.C.
     I.R.S. Identification Nos. of Above Person (entities only)
--------------------------------------------------------------------------------
2)   Check the Appropriate Box if a Member of a Group                    (a) [ ]
     (See Instructions)                                                  (b) [ ]
--------------------------------------------------------------------------------

3)   SEC Use Only
--------------------------------------------------------------------------------

4)   Citizenship or Place of Organization                               Delaware
--------------------------------------------------------------------------------
                        5)  Sole Voting Power                                  0
     Number of Shares   --------------------------------------------------------
     Beneficially       6)  Shared Voting Power                       13,092,353
     Owned by Each      --------------------------------------------------------
     Reporting          7)  Sole Dispositive Power                             0
     Person With        --------------------------------------------------------
                        8)  Shared Dispositive Power                  13,092,353
--------------------------------------------------------------------------------

9)   Aggregate Amount Beneficially Owned by Each Reporting Person     13,092,353
--------------------------------------------------------------------------------

10)  Check if the Aggregate Amount in Row (9) Excludes
     Certain Shares (See Instructions)                                       [ ]
--------------------------------------------------------------------------------

11)  Percent of Class Represented by Amount in Row 9                      56.52%
--------------------------------------------------------------------------------

12)  Type of Reporting Person (See Instructions)                              OO
--------------------------------------------------------------------------------


                                  Page 3 of 10



CUSIP N.. 112211107


--------------------------------------------------------------------------------
1)   Names of Reporting Person.                              CHARLES E. DAVIDSON
     I.R.S. Identification Nos. of Above Person (entities only)

--------------------------------------------------------------------------------
2)   Check the Appropriate Box if a Member of a Group                    (a) [ ]
     (See Instructions)                                                  (b) [ ]

--------------------------------------------------------------------------------
3)   SEC Use Only

--------------------------------------------------------------------------------
4)   Citizenship or Place of Organization                                 U.S.A.

--------------------------------------------------------------------------------
                        5)  Sole Voting Power                                  0
     Number of Shares   --------------------------------------------------------
     Beneficially       6)  Shared Voting Power                       13,092,353
     Owned by Each      --------------------------------------------------------
     Reporting          7)  Sole Dispositive Power                             0
     Person With        --------------------------------------------------------
                        8)  Shared Dispositive Power                  13,092,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     13,092,353

--------------------------------------------------------------------------------
10)  Check if the Aggregate Amount in Row (9) Excludes
     Certain Shares (See Instructions)                                       [ ]

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      56.52%

--------------------------------------------------------------------------------
12)  Type of Reporting Person (See Instructions)                              IN

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


                                  Page 4 of 10



CUSIP N. 112211107


--------------------------------------------------------------------------------
1)   Names of Reporting Person.                                 JOSEPH M. JACOBS
     I.R.S. Identification Nos. of Above Person (entities only)

--------------------------------------------------------------------------------
2)   Check the Appropriate Box if a Member of a Group                    (a) [ ]
     (See Instructions)                                                  (b) [ ]

--------------------------------------------------------------------------------
3)   SEC Use Only

--------------------------------------------------------------------------------
4)   Citizenship or Place of Organization                                 U.S.A.

--------------------------------------------------------------------------------
                        5)  Sole Voting Power                                  0
     Number of Shares       ----------------------------------------------------
     Beneficially       6)  Shared Voting Power                       13,092,353
     Owned by Each          ----------------------------------------------------
     Reporting          7)  Sole Dispositive Power                             0
     Person With            ----------------------------------------------------
                        8)  Shared Dispositive Power                  13,092,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     13,092,353

--------------------------------------------------------------------------------
10)  Check if the Aggregate Amount in Row (9) Excludes
     Certain Shares (See Instructions)                                       [ ]

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      56.52%

--------------------------------------------------------------------------------
12)  Type of Reporting Person (See Instructions)                              IN

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


                                  Page 5 of 10



CUSIP N. 112211107


     The reporting persons named in Item 2 below are hereby jointly filing this
Schedule 13G (this "STATEMENT") because due to certain affiliates and
relationships among the reporting persons, such reporting persons may be deemed
to beneficially own the same securities directly acquired from the Issuer named
in Item I below by one of the reporting persons. In accordance with Rule
13d-1(k)(1)(iii) promulgated pursuant to the Securities Exchange Act of 1934, as
amended (the "EXCHANGE ACT"), the reporting persons named in Item 2 below have
executed a written agreement relating to the joint filing of this Schedule 13G
(the "JOINT FILING Agreement"), a copy of which is annexed hereto as Exhibit I.
This Statement is being filed on behalf of the Reporting Persons for the period
ended December 31, 2005. The Reporting Persons acquired the shares of Common
Stock of the Issuer which are the subject of this Statement prior to the
Issuer's initial public offering ("IPO") and have not acquired any additional
securities of the Issuer since the date of the IPO.

ITEM 1.

     (a)  Name of Issuer:

          BRONCO DRILLING COMPANY, INC.

     (b)  Address of Issuer's Principal Executive Offices:

          14313 North May Avenue, Suite 100
          Oklahoma, OK 73134

ITEM 2.

     (a)  Name of Persons Filing (collectively, the "REPORTING PERSONS")

          (i)    Bronco Drilling Holdings, L.L.C.
          (ii)   Wexford Capital LLC
          (iii)  Charles E. Davidson
          (iv)   Joseph M. Jacobs

     (b)  Address of Principal Business Office, or, if none, Residence of
          Reporting Persons:

          c/o Wexford Capital LLC
          411 West Putnam Avenue
          Greenwich, Connecticut 06930.

     (c)  Citizenship:
          (i)    Bronco Drilling Holdings, L.L.C. - Delaware
          (ii)   Wexford Capital LLC - Connecticut
          (iii)  Charles E. Davidson - United States
          (iv)   Joseph M. Jacobs - United States

     (d)  Title of Class of Securities:

          Common Stock.

     (e)  CUSIP Number:

          112211107.

                                  Page 6 of 10



CUSIP N. 112211107


ITEM 3.   IF THIS STATEMENT IS FILED PURSUANT TO SS.SS.240.13D-1(B) OR
240.13D-2(B) OR (C), CHECK WHETHER THE PERSON FILING IS A: N/A

     (a)  [ ]    Broker or dealer registered under section 15 of the Act
(15 U.S.C. 78o).

     (b)  [ ]    Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c).

     (c)  [ ]    Insurance company as defined in section 3(a)(19) of the Act
(15 U.S.C. 78c).

     (d)  [ ]    Investment company registered under section 8 of the Investment
Company Act of 1940 (15 U.S.C. 80a-8).

     (e)  [ ]    An investment adviser in accordance with ss.240.13d- 1(b)
(1)(ii)(E).

     (f)  [ ]    An employee benefit plan or endowment fund in accordance with
ss.240.13d-1(b)(1)(ii)(F).

     (g)  [ ]    A parent holding company or control person in accordance with
ss.240.13d-1(b)(1)(ii)(G).

     (h)  [ ]    A savings association as defined in section 3(b) of the Federal
Deposit Insurance Act (12 U.S.C. 1813).

     (i)  [ ]    A church plan that is excluded from the definition of an
investment company under section 3(c)(14) of the Investment Company Act
of 1940 (15 U.S.C. 80a-3).

     (j)  [ ]    Group, in accordance with section ss.240.13d-1(b)(1)(ii)(J).

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.
[Information set forth below is on the basis of 23,165,368 shares of Common
Stock issued and outstanding, as reported in the Company's Form 10-Q filed
November 9, 2005].

     (i)  Bronco Drilling Holdings, L.L.C.
          (a)  Amount beneficially owned: 13,092,353
          (b)  Percent of class: 56.52%
          (c)  Number of shares as to which the person has:
               (i)   Sole power to vote or to direct the vote:                 0
               (ii)  Shared power to vote or to direct the vote:      13,092,353
               (iii) Sole power to dispose or to direct the disposition of:    0
               (iv)  Shared power to dispose or to direct the
                     disposition of:                                  13,092,353

     (ii) Wexford Capital LLC:
          (a)  Amount beneficially owned: 13,092,353
          (b)  Percent of class: 56.52%
          (c)  Number of shares as to which the person has:
               (i)   Sole power to vote or to direct the vote:                 0
               (ii)  Shared power to vote or to direct the vote:      13,092,353
               (iii) Sole power to dispose or to direct the disposition of:    0
               (iv)  Shared power to dispose or to direct the
                     disposition of:                                  13,092,353

     (iii) Charles E. Davidson:
          (a)  Amount beneficially owned: 13,092,353

                                  Page 7 of 10



CUSIP N. 112211107

          (b)  Percent of class: 56.52%
          (c)  Number of shares as to which the person has:
               (i)   Sole power to vote or to direct the vote:                 0
               (ii)  Shared power to vote or to direct the vote:      13,092,353
               (iii) Sole power to dispose or to direct the disposition of:    0
               (iv)  Shared power to dispose or to direct the
                     disposition of:                                  13,092,353

     (iv) Joseph M. Jacobs:
          (a)  Amount beneficially owned: 13,092,353
          (b)  Percent of class: 56.52%
          (c)  Number of shares as to which the person has:
               (i)   Sole power to vote or to direct the vote:                 0
               (ii)  Shared power to vote or to direct the vote:      13,092,353
               (iii) Sole power to dispose or to direct the disposition of:    0
               (iv)  Shared power to dispose or to direct the
                     disposition of:                                  13,092,353

Wexford Capital may, by reason of its status as manager of Bronco Drilling
Holdings, L.L.C. ("Bronco Holdings") be deemed to own beneficially the interest
in the shares of Common Stock of which Bronco Holdings possesses beneficial
ownership. Each of Charles E. Davidson and Joseph M. Jacobs may, by reason of
his status as a controlling person of Wexford Capital, be deemed to own
beneficially the interests in the shares of Common Stock of which Bronco
Holdings possesses beneficial ownership. Each of Charles E. Davidson, Joseph M.
Jacobs and Wexford Capital shares the power to vote and to dispose of the
interests in the shares of Common Stock beneficially owned by Bronco Holdings.
Each of Messrs. Davidson and Jacobs disclaims beneficial ownership of the shares
of Common Stock owned by Bronco Holdings and Wexford Capital.

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 / /. N/A

ITEM 6.   OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON:  N/A

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

          The 13,092,353 shares of the Common Stock of the Issuer in respect of
          which this Statement is being filed are held directly by Bronco
          Drilling Holdings, L.L.C., a company controlled indirectly by Wexford
          Capital LLC, which acts as its manager.

ITEM 8.   IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:  N/A

ITEM 9.   NOTICE OF DISSOLUTION OF GROUP:  N/A

                                  Page 8 of 10



CUSIP N. 112211107

ITEM 10.  CERTIFICATION.

After reasonable inquiry and to the best of each of the undersigned's knowledge
and belief, each of the undersigned certifies that the information set forth in
this statement is true, complete and correct.


Dated:    February 7, 2006

                                      BRONCO DRILLING HOLDINGS, L.L.C.


                                      By:  /s/ Arthur H. Amron
                                           -------------------------------------
                                           Name:  Arthur H. Amron
                                           Title: Vice President and Assistant
                                                  Secretary


                                      WEXFORD CAPITAL LLC

                                      By:  /s/ Arthur H. Amron
                                           -------------------------------------
                                           Name:  Arthur H. Amron
                                           Title: Principal and Secretary


                                           /s/ Charles E. Davidson
                                           -------------------------------------
                                           CHARLES E. DAVIDSON


                                           /s/ Joseph M. Jacobs
                                           -------------------------------------
                                           JOSEPH M. JACOBS


                                  Page 9 of 10



CUSIP N. 112211107


                                      JOINT FILING AGREEMENT


     Pursuant to Rule 13d-1(k)(1)(iii) of the Securities Exchange Act of 1934,
each of the undersigned agrees that a single joint Schedule 13G and any
amendments thereto may be filed on behalf of each of the undersigned with
respect to the securities held by each of them in Bronco Drilling Company, Inc.



                                      BRONCO DRILLING HOLDINGS, L.L.C.


                                      By:  /s/ Arthur H. Amron
                                           -------------------------------------
                                           Name:  Arthur H. Amron
                                           Title: Vice President and Assistant
                                                  Secretary


                                      WEXFORD CAPITAL LLC

                                      By:  /s/ Arthur H. Amron
                                           -------------------------------------
                                           Name:  Arthur H. Amron
                                           Title: Principal and Secretary


                                           /s/ Charles E. Davidson
                                           -------------------------------------
                                           CHARLES E. DAVIDSON


                                           /s/ Joseph M. Jacobs
                                           -------------------------------------
                                           JOSEPH M. JACOBS


                                  Page 10 of 10