<?xml version="1.0"?><?xml-stylesheet type="text/xsl" href="../4_X02.xsl"?><ownershipDocument>    <schemaVersion>X0303</schemaVersion>    <documentType>4</documentType>    <periodOfReport>2010-12-04</periodOfReport>    <notSubjectToSection16>0</notSubjectToSection16>    <issuer>        <issuerCik>0001018946</issuerCik>        <issuerName>STEINER LEISURE Ltd</issuerName>        <issuerTradingSymbol>STNR</issuerTradingSymbol>    </issuer>    <reportingOwner>        <reportingOwnerId>            <rptOwnerCik>0001128759</rptOwnerCik>            <rptOwnerName>FUSFIELD GLENN</rptOwnerName>        </reportingOwnerId>        <reportingOwnerAddress>            <rptOwnerStreet1>C/O STEINER MANAGEMENT SERVICES</rptOwnerStreet1>            <rptOwnerStreet2>770 S. DIXIE HIGHWAY - SUITE 200</rptOwnerStreet2>            <rptOwnerCity>CORAL GABLES</rptOwnerCity>            <rptOwnerState>FL</rptOwnerState>            <rptOwnerZipCode>33146</rptOwnerZipCode>            <rptOwnerStateDescription></rptOwnerStateDescription>        </reportingOwnerAddress>        <reportingOwnerRelationship>            <isDirector>0</isDirector>            <isOfficer>1</isOfficer>            <isTenPercentOwner>0</isTenPercentOwner>            <isOther>0</isOther>            <officerTitle>Executive VP &amp; COO - Maritime</officerTitle>        </reportingOwnerRelationship>    </reportingOwner>    <nonDerivativeTable>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Shares</value>            </securityTitle>            <transactionDate>                <value>2010-12-04</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>F</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>1350</value>                    <footnoteId id="F1"/>                </transactionShares>                <transactionPricePerShare>                    <value>42.23</value>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>20507</value>                    <footnoteId id="F2"/>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>        <nonDerivativeTransaction>            <securityTitle>                <value>Common Shares</value>            </securityTitle>            <transactionDate>                <value>2010-12-08</value>            </transactionDate>            <deemedExecutionDate></deemedExecutionDate>            <transactionCoding>                <transactionFormType>4</transactionFormType>                <transactionCode>S</transactionCode>                <equitySwapInvolved>0</equitySwapInvolved>            </transactionCoding>            <transactionTimeliness>                <value></value>            </transactionTimeliness>            <transactionAmounts>                <transactionShares>                    <value>8998</value>                </transactionShares>                <transactionPricePerShare>                    <value>42.0048</value>                    <footnoteId id="F3"/>                </transactionPricePerShare>                <transactionAcquiredDisposedCode>                    <value>D</value>                </transactionAcquiredDisposedCode>            </transactionAmounts>            <postTransactionAmounts>                <sharesOwnedFollowingTransaction>                    <value>11509</value>                    <footnoteId id="F2"/>                </sharesOwnedFollowingTransaction>            </postTransactionAmounts>            <ownershipNature>                <directOrIndirectOwnership>                    <value>D</value>                </directOrIndirectOwnership>            </ownershipNature>        </nonDerivativeTransaction>    </nonDerivativeTable>    <footnotes>        <footnote id="F1">Shares withheld to satisfy the reporting person's tax withholding obligation upon the vesting of restricted shares.</footnote>        <footnote id="F2">Includes restricted shares and restricted share units that have not yet vested.</footnote>        <footnote id="F3">Weighted average from 22 transactions with prices ranging from a low of $42.00 to a high of $42.04.  The reporting person undertakes to provide, upon request, full information regarding the number of shares sold at each separate price.</footnote>    </footnotes>    <remarks></remarks>    <ownerSignature>        <signatureName>/s/ Glenn Fusfield</signatureName>        <signatureDate>2010-12-08</signatureDate>    </ownerSignature></ownershipDocument>