How to best detect encoding in XML file?

Ok, I should have thought of this earlier. Both XmlTextReader (which gives us the Encoding) and XmlReader.Create (which allows us to specify encoding) accepts a Stream. So how about first opening a FileStream and then use this with both XmlTextReader and XmlReader, like this:

using (var txtreader = new FileStream(filepath, FileMode.Open))
{
    using (var xmlreader = new XmlTextReader(txtreader))
    {
        // Read in the encoding info
        xmlreader.MoveToContent();
        var encoding = xmlreader.Encoding;

        // Rewind to the beginning
        txtreader.Seek(0, SeekOrigin.Begin);

        var settings = new XmlReaderSettings { NameTable = new NameTable() };
        var xmlns = new XmlNamespaceManager(settings.NameTable);
        var context = new XmlParserContext(null, xmlns, "", XmlSpace.Default,
                 encoding);

        using (var reader = XmlReader.Create(txtreader, settings, context))
        {
            return XElement.Load(reader);
        }
    }
}

This works like a charm. Reading XML files in an encoding independent way should have been more elegant but at least I'm getting away with only one file open.