<?xml version="1.0"?>

<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2004-01-14</periodOfReport>


    <noSecuritiesOwned>1</noSecuritiesOwned>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001256424</rptOwnerCik>
            <rptOwnerName>PRESUTTI LUIS I</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1></rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity></rptOwnerCity>
            <rptOwnerState></rptOwnerState>
            <rptOwnerZipCode></rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>ASSISTANT TREASURER</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>



    <ownerSignature>
        <signatureName>LUIS PRESUTTI</signatureName>
        <signatureDate>2004-01-14</signatureDate>
    </ownerSignature>

</ownershipDocument>

