**Exhibit
      31.2**




**CERTIFICATION**




I,
      Zachary M. Graves, Chief Financial Officer of Bronco Drilling Company, Inc.,
      certify that:




1.
      I have
      reviewed this quarterly report on Form 10-Q of Bronco Drilling Company, Inc.;




2.
      Based
      on my knowledge, this report does not contain any untrue statement of a material
      fact or omit to state a material fact necessary to make the statements made,
      in
      light of the circumstances under which such statements were made, not misleading
      with respect to the period covered by this report;




3.
      Based
      on my knowledge, the financial statements, and other financial information
      included in this report, fairly present in all material respects the financial
      condition, results of operations and cash flows of the registrant as of, and
      for, the periods presented in this report;




4.
      The
      registrant’s other certifying officer and I are responsible for establishing and
      maintaining disclosure controls and procedures (as defined in Exchange Act
      Rules
      13a-15(e) and 15d-15(e)) and internal control over financial reporting (as
      defined in Exchange Act Rules 13(a)-15(f) and 15(d)-15(f)) for the registrant
      and have:




(a)
      Designed such disclosure controls and procedures, or caused such disclosure
      controls and procedures to be designed under our supervision, to ensure that
      material information relating to the registrant, including its consolidated
      subsidiaries, is made known to us by others within those entities, particularly
      during the period in which this report is being prepared;




(b)
      Designed such internal controls over financial reporting, or caused such
      internal control over financial reporting to be designed under our supervision,
      to provide reasonable assurance regarding the reliability of financial reporting
      and the preparation of financial statements for external purposes in accordance
      with generally accepted accounting principles;




(c)
      Evaluated the effectiveness of the registrant’s disclosure controls and
      procedures and presented in this report our conclusions about the effectiveness
      of the disclosure controls and procedures, as of the end of the period covered
      by this report based on such evaluation; and




(d)
      Disclosed in this report any change in the registrant’s internal control over
      financial reporting that occurred during the registrant’s most recent fiscal
      quarter (the registrant’s fourth fiscal quarter in the case of an annual report)
      that has materially affected, or is reasonably likely to materially affect,
      the
      registrant’s internal control over financial reporting; and




5.
      The
      registrant’s other certifying officer and I have disclosed, based on our most
      recent evaluation of internal control over financial reporting, to the
      registrant’s auditors and the audit committee of the registrant’s board of
      directors (or persons performing the equivalent functions):




(a)
      All
      significant deficiencies and material weaknesses in the design or operation
      of
      internal control over financial reporting which are reasonably likely to
      adversely affect the registrant’s ability to record, process, summarize and
      report financial information; and




(b)
      Any
      fraud, whether or not material, that involves management or other employees
      who
      have a significant role in the registrant’s internal control over financial
      reporting.




Date:
      May
      9, 2007




/S/
                ZACHARYM.
                GRAVES**Zachary
                M. Graves****Chief
                Financial Officer**