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So far its not posible with thunderbird as far as i know.
BUT!
You can use other tools and for example auto execute Thunderbird when new mail comes in.
Check out: http://www.poptray.org/
I use it for my work mostly with just a sound notify which is enough for me.
So far, on 10.000 test mails it does not crash 
There are others:
http://sniperbeamer.de/tbtray/
and
https://addons.mozilla.org/en-US/thunderbird/addon/2110
“Science is the belief in the ignorance of the experts” - Richard P. Feynman
Are those things portable???
------------------
I don't have a signature
Should I have a signature?
If a packet hits a pocket on a socket on a port,
and the bus is interrupted as a very last resort,
and the address of the memory makes your floppy disk abort,
then the socket packet pocket has an error to report 
Tbtray and the only thing it left was:
C:\WINDOWS\system32\config\software.LOG C:\WINDOWS\system32\config\system.LOG C:\WINDOWS\system32\wbem\Repository\FS\INDEX.BTR C:\WINDOWS\system32\wbem\Repository\FS\INDEX.MAP C:\WINDOWS\system32\wbem\Repository\FS\MAPPING.VER C:\WINDOWS\system32\wbem\Repository\FS\MAPPING1.MAP C:\WINDOWS\system32\wbem\Repository\FS\OBJECTS.DATA C:\WINDOWS\system32\wbem\Repository\FS\OBJECTS.MAP
But this could also been left by TB so I think it is fully portable.
I think wbem has something to do with internet.
It would be cool if the same would exist for FF.
“Science is the belief in the ignorance of the experts” - Richard P. Feynman
I get the little icon on the systray that there are new messages, when there are new messages.
"... respect, all good works are not done by only good folk. For here, at the end of all things, we shall do what needs to be done." --till next time, Jameson Stalanthas Yu -x-
elaborate?
“Science is the belief in the ignorance of the experts” - Richard P. Feynman
I've always had it. I think it is part of TB, where you can have in account settings to always check for new mail, I set it for 10 minutes. As long as I have TB open, but mimnimized, it always checks and give me a little icon in my systray. Good enough for me.
May not be what you were looking for though. I've tried the little minimize to systray add-ons from mozilla.com, but I decided that I didn't want to add another thing to load up automatically at startup.
"... respect, all good works are not done by only good folk. For here, at the end of all things, we shall do what needs to be done." --till next time, Jameson Stalanthas Yu -x-
The functionality the "minimize to tray addon" provides is exactly what the original poster wants. Not having a minimized window but nothing but a small icon in the systray.
“Science is the belief in the ignorance of the experts” - Richard P. Feynman
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