**Exhibit
      10.4**





AMENDMENT
      TO EMPLOYMENT AGREEMENT





This
      Amendment to Employment Agreement is made effective as of August 2, 2007 by
      and
      between Bronco Drilling Company, Inc., a Delaware corporation (the “ ***Company*** ”),
      and
      Zachary M. Graves, an individual (the “ ***Executive*** ”).
      Terms
      used but not otherwise defined herein shall have the meaning set forth in that
      certain Employment Agreement, dated as of August 8, 2006, by and between the
      Company and the Executive (the “ ***Employment
      Agreement*** ”).





WHEREAS,
      the Company and the Executive desire to modify the Employment Agreement pursuant
      to Section 11.5 thereof.





NOW,
      THEREFORE, in consideration of the mutual promises contained herein, and for
      other good and valuable consideration, the receipt and sufficiency of which
      is
      hereby acknowledged, the Company and the Executive hereto agree as
      follows:




1.  Section
      2.2 of the Employment Agreement is hereby amended and restated in its entirety
      to read as follows:





**2.2**  **Modifications** .
      The
      precise duties to be performed by the Executive may be extended or curtailed
      in
      the discretion of the Board. However, the occurrence of any one or more of
      the
      following events (such events, individually and collectively, “ ***Good
      Reason*** ”)
      shall
      constitute termination without Cause (as hereinafter defined): (a) a
      reduction in the Executive’s then current Base Salary (as hereinafter defined)
      or a significant reduction in the Executive’s then current benefits as provided
      in Section 4 hereof; (b) a demotion by means of a reduction in
      authority, responsibilities, duties or titles to a position of less stature
      or
      importance with the Company or an assignment of duties materially inconsistent
      with the Executive’s position, authority, duties or responsibility; (c) the
      Company’s principal executive officers are moved to a location more than 25
      miles from its current location or the Executive is required to be based
      anywhere other than the Company’s principal executive offices; (d) a
      failure by the Company to require any successor to the Company or to all or
      substantially all of the business or assets of the Company to expressly assume
      the obligations of the Company under this Agreement; or (e) a breach by the
      Company of a material provision of this Agreement or any other material plan
      or
      program covering the Executive.




2.  Section
      2.2 of the Employment Agreement is hereby amended by the addition of the
      following sentence to the end of Section 2.2:





Notwithstanding
      anything in this Agreement to the contrary, in the event the Executive provides
      written notice to the Company that he is terminating his employment for Good
      Reason, other than in connection with a termination upon a Change of Control
      (as
      hereinafter defined), the Executive shall receive the termination compensation
      provided in Section 6.1(a) hereof within ten (10) days of receipt by the Company
      of written notice of such termination.





3.  Section
      6.3 of the Employment Agreement is hereby amended and restated in its entirety
      to read as follows:





**6.3**  **Termination
      in Connection with a Change of Control** .
      The
      Executive will be entitled to terminate this Agreement with or without Cause
      or
      Good Reason at anytime within two (2) years following a Change of Control by
      providing written notice to the Company (or any successor to the Company or
      any
      parent corporation of the Company). Within ten (10) days of the Company’s (or
      any successor to the Company or any parent corporation of the Company) receipt
      of such notice, the Executive shall receive a severance payment (in addition
      to
      any other rights and other amounts payable to the Executive under Section 6.7
      or
      under Company plans in which the Executive is a participant) payable in a lump
      sum in cash an amount equal to the sum of the following: (i) three (3) times
      the
      sum of the Executive’s highest paid annual Base Salary plus the bonus paid
      pursuant to Section 4.2 (based on the average of the last three years’ annual
      bonuses or such lesser number of years as the Executive may have been employed);
      plus (ii) any applicable Gross-Up Payment. If the foregoing amount is not paid
      within ten (10) days after the notice of such termination is received by the
      Company, the unpaid amount will bear interest at the per annum rate of 12%
      per
      annum. Notwithstanding the foregoing, if at the time of such termination the
      Executive is a “specified employee” as defined in regulations under Section 409A
      of the Code, such payment will be made on the first day which is more than
      six
      (6) months following the termination. In connection with any Change of Control,
      the Company shall obtain the assumption of this Agreement, without limitation
      or
      reduction, by any successor to the Company or any parent corporation of the
      Company. In the event the Company (or any successor to the Company or any parent
      corporation of the Company) terminates this Agreement, with or without Cause,
      within two (2) years following a Change of Control, the Executive shall be
      entitled to the severance payment set forth in this Section 6.3 on the same
      terms as if the Executive elected to terminate this Agreement under this Section
      6.3.




For
      the
      purpose of this Agreement, a “ ***Change
      of Control*** ”
means
      the occurrence of any of the following events:




(a)  The
      acquisition by any individual, entity or group (within the meaning of Section
      13(d)(3) or 14(d)(2) of the Securities Exchange Act of 1934, as amended (the
      “ ***Exchange
      Act*** ”))
      (a
“ ***Person*** ”), of
      beneficial ownership (within the meaning of Rule 13d-3 promulgated under
      the Exchange Act) of 40% or more of either (i) the then outstanding shares
      of
      common stock of the Company (the “ ***Outstanding
      Company Common Stock*** ”)
      or
      (ii) the combined voting power of the then outstanding voting securities of
      the
      Company entitled to vote generally in the election of directors (the
“ ***Outstanding
      Company Voting Securities*** ”).
      For
      purposes of this Section 6.3(a), any acquisition by any employee benefit plan
      (or related trust) sponsored or maintained by the Company or any corporation
      controlled by the Company will not constitute a Change in Control.




(b)  The
      individuals who, as of the date hereof, constitute the Board (the “ ***Incumbent
      Board*** ”)
      cease
      for any reason to constitute at least a majority of the Board. Any individual
      becoming a director subsequent to the date hereof whose election, or nomination
      for election by the Company’s stockholders, is approved by a vote of at least a
      majority of the directors then comprising the Incumbent Board will be considered
      a member of the Incumbent Board as of the date hereof, but any such individual
      whose initial assumption of office occurs as a result of an actual or threatened
      election contest with respect to the election or removal of directors or other
      actual or threatened solicitation of proxies or consents by or on behalf of
      a
      Person other than the Incumbent Board will not be deemed a member of the
      Incumbent Board as of the date hereof.




(c)  The
      consummation of a reorganization, merger, consolidation or sale or other
      disposition of all or substantially all of the assets of the Company (a
“ ***Business
      Combination*** ”),
      unless following such Business Combination: (i) the individuals and entities
      who
      were the beneficial owners, respectively, of the Outstanding Company Common
      Stock and Outstanding Company Voting Securities immediately prior to such
      Business Combination beneficially own, directly or indirectly, more than 60%
      of,
      respectively, the then outstanding shares of common stock and the combined
      voting power of the then outstanding voting securities entitled to vote
      generally in the election of directors, as the case may be, of the corporation
      resulting from such Business Combination (including, without limitation, a
      corporation which, as a result of such transaction, owns the Company or all
      or
      substantially all of the Company’s assets either directly or through one ore
      more subsidiaries) in substantially the same proportions as their ownership,
      immediately prior to such Business Combination of the Outstanding Company Common
      Stock and Outstanding Company Voting Securities, as the case may be; (ii) no
      Person (excluding any corporation resulting from such Business Combination
      or
      any employee benefit plan (or related trust) of the Company or such corporation
      resulting from such Business Combination) beneficially owns, directly or
      indirectly, 40% or more of, respectively, the then outstanding shares of common
      stock of the corporation resulting from such Business Combination or the
      combined voting power of the then outstanding voting securities of such
      corporation except to the extent that such ownership existed prior to the
      Business Combination; and (iii) at least a majority of the members of the board
      of directors of the corporation resulting from such Business Combination were
      members of the Incumbent Board at the time of the execution of the initial
      agreement, or of the action of the Board, providing for such Business
      Combination.




(d)  The
      approval by the stockholders of the Company of a complete liquidation or
      dissolution of the Company.


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4.  The
      terms
      and provisions of the Employment Agreement shall remain in full force and effect
      except as amended hereby.





*****  -2-





IN
      WITNESS WHEREOF, the undersigned have executed this Amendment
      to Employment Agreement effective the date first above written.




**THE
      COMPANY:**





BRONCO
      DRILLING
      COMPANY, INC.








By: /s/
      MARK DUBBERSTEIN


Mark Dubberstein, President











**THE
      EXECUTIVE:**








/s/
      ZACHARY M.
      GRAVES


Zachary
      M.
      Graves





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