<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2005-12-20</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001022705</issuerCik>
        <issuerName>TESCO CORP</issuerName>
        <issuerTradingSymbol>TESOF</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001218321</rptOwnerCik>
            <rptOwnerName>OSS CAPITAL MANAGEMENT</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>605 THIRD AVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10158</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2005-12-20</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>0</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This Form 4 is being filed to report that O.S.S. Capital Management LP, a Delaware limited partnership (the &quot;Investment
 Manager&quot;), Schafer Brothers LLC, a Delaware limited liability company (the &quot;SB LLC&quot;), Mr. Oscar S. Schafer (&quot;Mr. Schafer&quot;),
 Mr. Andrew Goffe (&quot;Mr. Goffe) and Mr. Brad Rosenberg (&quot;Mr. Rosenberg&quot;, collectively with the Investment Manager, SB LLC, Mr.
 Schafer and Mr. Goffe, the &quot;Reporting Persons&quot;) disclaim beneficial ownership of Tesco Corp's (the &quot;Issuer&quot;) securities for
 the purposes of Section 16.  The purchased securities reported in Form 3 filed on November 16, 2005 (Accession Number:
 0000902664-05-002242) and subsequent Form 4s filed on November 17, 2005, November 18, 2005 and November 21, 2005 (Accession
 Numbers:  0000902664-05-002243, 0000902664-05-002253, 0000902664-05-002258 and  0000902664-05-002265)

*** Footnote (1) is continued in its entirety in Remark (1).</footnote>
    </footnotes>

    <remarks>Footnote (1) continued.

were not required to be filed in accordance with Rule 3a12-3 of the U.S. Securities Exchange Act of 1934 (the &quot;Exchange
 Act&quot;), as amended, as the Issuer falls under the definition provided in Rule 3b-4 of the Exchange Act.

This report shall not be deemed an admission that the Reporting Persons are or have been the beneficial owners of such
 securities for purposes of Section 16 or for any other purpose. The Reporting Persons hereby check the box and are not
 subject to further reporting requirements of Section 16.</remarks>

    <ownerSignature>
        <signatureName>/s/ Oscar S. Schafer</signatureName>
        <signatureDate>2005-12-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
