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

                                  SCHEDULE 13G

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 1)*


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

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

                                    112211107
                                    ---------
                                 (CUSIP Number)

                                 March 29, 2006
                                 --------------
             (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 9



CUSIP No. 112211107

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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

--------------------------------------------------------------------------------
     Number of Shares    5)   Sole Voting Power                                0
     Beneficially      ---------------------------------------------------------
     Owned by Each       6)   Shared Voting Power                     11,342,353
     Reporting         ---------------------------------------------------------
     Person With         7)   Sole Dispositive Power                           0
                       ---------------------------------------------------------
                         8)   Shared Dispositive Power                11,342,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     11,342,353

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

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      45.48%

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

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                                  Page 2 of 9


CUSIP No. 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

--------------------------------------------------------------------------------
     Number of Shares      5)    Sole Voting Power                             0
     Beneficially       --------------------------------------------------------
     Owned by Each         6)    Shared Voting Power                  11,342,353
     Reporting          --------------------------------------------------------
     Person With           7)    Sole Dispositive Power                        0
                        --------------------------------------------------------
                           8)    Shared Dispositive Power             11,342,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     11,342,353

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

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      45.48%

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

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

                                  Page 3 of 9



CUSIP No. 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.

--------------------------------------------------------------------------------
     Number of Shares      5)   Sole Voting Power                              0
     Beneficially       --------------------------------------------------------
     Owned by Each         6)   Shared Voting Power                   11,342,353
     Reporting          --------------------------------------------------------
     Person With           7)   Sole Dispositive Power                         0
                        --------------------------------------------------------
                           8)   Shared Dispositive Power              11,342,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     11,342,353

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

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      45.48%

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

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

                                  Page 4 of 9



CUSIP No. 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.

--------------------------------------------------------------------------------
     Number of Shares      5)    Sole Voting Power                             0
     Beneficially       --------------------------------------------------------
     Owned by Each         6)    Shared Voting Power                  11,342,353
     Reporting          --------------------------------------------------------
     Person With           7)    Sole Dispositive Power                        0
                        --------------------------------------------------------
                           8)    Shared Dispositive Power             11,342,353
--------------------------------------------------------------------------------
9)   Aggregate Amount Beneficially Owned by Each Reporting Person     11,342,353

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

--------------------------------------------------------------------------------
11)  Percent of Class Represented by Amount in Row 9                      45.48%

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

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

                                  Page 5 of 9


CUSIP No. 112211107

         This Amendment No. 1 to Schedule 13G modifies and supplements the
Schedule 13G initially filed on behalf of the reporting persons named in Item 2
below with the Securities and Exchange Commission on February 7, 2006 (the
"STATEMENT"). Except to the extent supplemented by the information contained in
this Amendment No. 1, the Statement, as amended as provided herein, remains in
full force and effect. Capitalized terms used herein without definition have the
respective meanings ascribed to them in the Statement.

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.

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).

                                   Page 6 of 9



CUSIP No. 112211107

     (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 24,937,939 shares of Common Stock issued
     and outstanding, following the closing of the sale of Shares described in
     the Company's Prospectus, filed with the Securities and Exchange Commission
     on March 24, 2006].




     (i)   Bronco Drilling Holdings, L.L.C.
           (a)    Amount beneficially owned: 11,342,353
           (b)    Percent of class: 45.48%
           (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:                11,342,353
                  (iii)  Sole power to dispose or to direct the disposition of:     0
                  (iv)   Shared power to dispose or to direct the disposition of:   11,342,353

     (ii)  Wexford Capital LLC:
           (a)    Amount beneficially owned: 11,342,353
           (b)    Percent of class: 45.48%
           (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:                 11,342,353
                  (iii)  Sole power to dispose or to direct the disposition of:      0
                  (iv)   Shared power to dispose or to direct the disposition of:    11,342,353

     (iii) Charles E. Davidson:
           (a)    Amount beneficially owned: 11,342,353
           (b)    Percent of class: 45.48%
           (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:                 11,342,353
                  (iii)  Sole power to dispose or to direct the disposition of:      0
                  (iv)   Shared power to dispose or to direct the disposition of:    11,342,353


                                  Page 7 of 9


CUSIP No. 112211107




     (iv)  Joseph M. Jacobs:
           (a)    Amount beneficially owned: 11,342,353
           (b)    Percent of class: 45.48%
           (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:                 11,342,353
                  (iii)  Sole power to dispose or to direct the disposition of:      0
                  (iv)   Shared power to dispose or to direct the disposition of:    11,342,353


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 11,342,353 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 9



CUSIP No. 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:     March 29, 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 9