SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934
(Amendment No. 3)*

BRONCO DRILLING COMPANY, INC.

(Name of Issuer)

Shares of Common Stock, par value $.01 per share
(Title of Class of Securities)

112211107
(CUSIP Number)

Arthur H. Amron, Esq.
Wexford Capital LLC
411 West Putnam Avenue
Greenwich, CT 06830
(203) 862-7012
(Name, Address and Telephone Number of Person Authorized to
Receive Notices and Communications)

— with copies to —
Gregg Berman, Esq.
Fulbright & Jaworski L.L.P.
666 Fifth Avenue
New York, NY 10103
(212) 318-3000

August 5, 2008
(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of Rule 13d-1(e), Rule 13d-1(f) or Rule 13d-1(g), check the following box.o

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See section 240.13d-7 for other parties to whom copies are to be sent.

* 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 other subject to the liabilities of that section of Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 112211107 Page 2

     This Amendment No. 3 to Schedule 13D modifies and supplements the Schedule 13D initially filed on July 25, 2008, as amended (the “Statement”), with respect to the common stock, $0.01 par value per share (the “Common Stock”), of Bronco Drilling Company, Inc. (the “Company”). Except to the extent supplemented by the information contained in this Amendment No. 3, the Statement, as previously amended and 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 4. Purpose of Transaction.

     The third paragraph of Item 4 of the Statement is hereby amended by the addition of the following:

     On August 5, 2008 the Reporting Persons issued a press release regarding the Merger Agreement. A copy of that press release is attached hereto as Exhibit 99.5.

Item 7. Materials to be filed as exhibits

     Item 7 of the Statement is hereby amended by the addition of the following:

     Exhibit 99.5      Press Release from Wexford Capital LLC dated August 5, 2008

* * * * *

CUSIP No. 112211107 Page 3

SIGNATURE

     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 Amendment No. 3 is true, complete and correct.

Dated: August 5, 2008

WEXFORD ALPHA TRADING LIMITED
By:	/s/ Arthur Amron
Name:	Arthur Amron
Title:	Vice President
WEXFORD CATALYST INVESTORS LLC
By:	/s/ Arthur Amron
Name:	Arthur Amron
Title:	Vice President and Assistant Secretary
WEXFORD SPECTRUM TRADING LIMITED
By:	/s/ Arthur Amron
Name:	Arthur Amron
Title:	Vice President
WEXFORD CAPITAL LLC
By:	/s/ Arthur Amron
Name:	Arthur Amron
Title:	Partner and Secretary
/s/ Charles E. Davidson
Charles E. Davidson
/s/ Joseph M. Jacobs
Joseph M. Jacobs

CUSIP No. 112211107 Page 4

Exhibit Index

Exhibit 99.5 Press Release from Wexford Capital LLC dated August 5, 2008