-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 HsEUQhJ0XF/Zu/7PuSVuuVhnhfuxWYnYiBfp4GoNo30XH2U3EvfSantR7wfcNJwK
 /9Rr+pgKT+3CNvkeDPbOSQ==

<SEC-DOCUMENT>0001140361-08-023024.txt : 20081010
<SEC-HEADER>0001140361-08-023024.hdr.sgml : 20081010
<ACCEPTANCE-DATETIME>20081010165519
ACCESSION NUMBER:		0001140361-08-023024
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20081008
FILED AS OF DATE:		20081010
DATE AS OF CHANGE:		20081010

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			JACOBS JOSEPH
		CENTRAL INDEX KEY:			0001048485

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-51471
		FILM NUMBER:		081118788

	BUSINESS ADDRESS:	
		BUSINESS PHONE:		203-862-7000

	MAIL ADDRESS:	
		STREET 1:		411 W PUTNAM AVENUE
		CITY:			GREENWICH
		STATE:			CT
		ZIP:			06830

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Bronco Drilling Company, Inc.
		CENTRAL INDEX KEY:			0001328650
		STANDARD INDUSTRIAL CLASSIFICATION:	DRILLING OIL & GAS WELLS [1381]
		IRS NUMBER:				202902156
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		16217 NORTH MAY AVENUE
		CITY:			EDMOND
		STATE:			OK
		ZIP:			73013
		BUSINESS PHONE:		405.242.4444

	MAIL ADDRESS:	
		STREET 1:		16217 NORTH MAY AVENUE
		CITY:			EDMOND
		STATE:			OK
		ZIP:			73013

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			DAVIDSON CHARLES E
		CENTRAL INDEX KEY:			0001001391

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-51471
		FILM NUMBER:		081118789

	BUSINESS ADDRESS:	
		STREET 1:		411 WEST PUTNAM AVE
		CITY:			GREENWICH
		STATE:			CT
		ZIP:			06830
		BUSINESS PHONE:		2028627400

	MAIL ADDRESS:	
		STREET 1:		C/O WEXFORD MANAGEMENT LLC
		STREET 2:		411 WEST PUTNAM AVE
		CITY:			GREENWICH
		STATE:			CT
		ZIP:			06830

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			WEXFORD CAPITAL LLC
		CENTRAL INDEX KEY:			0001048462
		STATE OF INCORPORATION:			DE
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-51471
		FILM NUMBER:		081118790

	BUSINESS ADDRESS:	
		STREET 1:		411 W PUTNAM AVENUE
		CITY:			GREENWICH
		STATE:			CT
		ZIP:			06830
		BUSINESS PHONE:		2038627000

	MAIL ADDRESS:	
		STREET 1:		411 W PUTNAM AVENUE
		CITY:			GREENWICH
		STATE:			CT
		ZIP:			06830

	FORMER NAME:	
		FORMER CONFORMED NAME:	WEXFORD MANAGEMENT LLC
		DATE OF NAME CHANGE:	19971024
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc1.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2008-10-08</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001328650</issuerCik>
        <issuerName>Bronco Drilling Company, Inc.</issuerName>
        <issuerTradingSymbol>BRNC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048462</rptOwnerCik>
            <rptOwnerName>WEXFORD CAPITAL LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>411 WEST PUTNAM AVENUE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 125</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001001391</rptOwnerCik>
            <rptOwnerName>DAVIDSON CHARLES E</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LLC</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVE.</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001048485</rptOwnerCik>
            <rptOwnerName>JACOBS JOSEPH</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WEXFORD CAPITAL LLC</rptOwnerStreet1>
            <rptOwnerStreet2>411 WEST PUTNAM AVENUE</rptOwnerStreet2>
            <rptOwnerCity>GREENWICH</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06830</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <transactionDate>
                <value>2008-10-08</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>101700</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>7.55</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2208819</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By: Wexford Spectrum Trading Limited</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These securities are owned solely by Wexford Spectrum Trading Limited (?WST?). Wexford Alpha Trading Limited (?WAT?) and Wexford Catalyst Investors LLC (?WCI?) affiliates of WST own 71,200 and 1,306,959 shares of Common Stock, respectively. Wexford Capital LLC (?Wexford?), as manager or investment sub advisor of WCI, WAT and WST, may be deemed to beneficially own the securities.  Charles E. Davidson (?Davidson?) and Joseph M. Jacobs (?Jacobs?) are the managing members of Wexford.  Davidson and Jacobs may also be deemed to beneficially own the securities.  Wexford, Davidson and Jacobs each disclaims beneficial ownership of the securities reported hereby and this report shall not be deemed as an admission that they are the beneficial owners of such securities except in the case of Davidson and Jacobs to the extent of their interests in WCI, WAT or WST.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Arthur H. Amron, Partner and Secretary of Wexford Capital LLC</signatureName>
        <signatureDate>2008-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Charles E. Davidson</signatureName>
        <signatureDate>2008-10-10</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Joseph M. Jacobs</signatureName>
        <signatureDate>2008-10-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
-----END PRIVACY-ENHANCED MESSAGE-----