Bronco Drilling 10-Q 2008 Q3 Quarterly report

Exhibit 32.2

CERTIFICATION OF PERIODIC REPORT

I, Zachary M. Graves, the Chief Financial Officer of Bronco Drilling Company, Inc. (the “Company”), certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that, to the best of my knowledge:

(i) the Quarterly Report on Form 10-Q of the Company for the quarter ended June 30, 2008 (the “Form 10-Q”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended (15 U.S.C. 78m(a) or 78o(d)); and

(ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 8, 2008

/S/ ZACHARY M. GRAVES

Zachary M. Graves

Chief Financial Officer

A signed original of this written statement required by Section 906 has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.