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

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2004-05-24</periodOfReport>

    <noSecuritiesOwned>1</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000069407</issuerCik>
        <issuerName>PIONEER INTEREST SHARES</issuerName>
        <issuerTradingSymbol>MUO</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000935485</rptOwnerCik>
            <rptOwnerName>WOLIN MARTIN J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1></rptOwnerStreet1>
            <rptOwnerStreet2>60 STATE STREET</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02109</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Compliance Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <ownerSignature>
        <signatureName>Martin J. Wolin</signatureName>
        <signatureDate>2005-05-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
