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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2006-05-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001352713</issuerCik>
        <issuerName>RAM Holdings Ltd.</issuerName>
        <issuerTradingSymbol>RAMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001260103</rptOwnerCik>
            <rptOwnerName>GREENWICH STREET INVESTMENTS II LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>500 CAMPUS DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 220</rptOwnerStreet2>
            <rptOwnerCity>FLORHAM PARK,</rptOwnerCity>
            <rptOwnerState>NJ</rptOwnerState>
            <rptOwnerZipCode>07932</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Shares</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3250000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">See attached Exhibit 99, Footnote (1)</footnote>
        <footnote id="F2">See attached Exhibit 99, Footnote (2)</footnote>
    </footnotes>

    <remarks>Remarks:
Exhibit List

Exhibit 99 - Explanation of Responses</remarks>

    <ownerSignature>
        <signatureName>Greenwich Street Investments II, L.L.C.                                                                           Name:  /s/ Matthew C. Kaufman,                                                                   Title: Managing Member</signatureName>
        <signatureDate>2006-05-10</signatureDate>
    </ownerSignature>
</ownershipDocument>
