using (Stream XmlPartStream = new MemoryStream())
using (XmlTextWriter XmlPartWriter = new XmlTextWriter(XmlPartStream, Encoding.Unicode))
{
    XDocument TheXInvoice = TheInvoice.XInvoice(dtInvoiceLines);
    XmlPartWriter.Formatting = Formatting.Indented;//xml output will be pretty-printed
    TheXInvoice.WriteTo(XmlPartWriter);//write to the MemoryStream
    XmlPartWriter.Flush();//finish writing to MemoryStream

    XmlPartStream.Seek(0, SeekOrigin.Begin);//rewind stream (Position=0 would also work)
    Attachment XmlPart = new Attachment(XmlPartStream, InvoiceXmlName, "application/xml");
    TheMail.Attachments.Add(XmlPart);
    XmlPartStream.Flush();//finish writing from MemoryStream to Attachment
    // BUG: no bytes in the Attachment

    XmlPartStream.Seek(0, SeekOrigin.Begin);//rewind stream (Position=0 would also work)
    byte[] ZippedXml = LempelZiv.GZip(XmlPartStream);
    // OK: Entire XML in the ZippedXml