I am now running TB 2.0.0.6 but I'm pretty sure this was
doing the same in earlier versions, only now I have
figured out exactly what is happening.

These screen shots will show my set up:

http://i12.tinypic.com/4lzekaf.jpg

http://i17.tinypic.com/6byd54p.jpg

This is a conventional ISP with a dailup connection, not Gmail.

Here is the situation:

Normally, email gets taken off the server after it is downloaded.

When an incoming email is truncated for being too large,
it is left on the server. If I click the link to download the
whole thing, it does so.

After I delete or move such a message from my Inbox
(whether I have downloaded the whole thing or not),
the message is still on the server.

The only way I know to get it off the server is to go in via
the ISP's web interface (i.e. not using TB).

Is there some way to get TB to handle this automatically?

Thank you.