exim headaches

[David Bellows <bfootdav@bellsouth.net>]

Hello everyone,

I've been banging my head against the wall on this one.  Here's what I'm
trying to do.

I have exim installed
I want local mail delivered locally like:
MAIL TO user1@thisbox FROM me@thisbox

In other words all local mail stays local.  This is currently working
with all the addresses being formed correctly so that a reply stays
local.

I want outgoing mail to be delivered
MAIL TO somone@isp.net FROM bfootdav@bellsouth.net # my real email
address

This is where the system fails.  It uses my local address as the origin
and REPLY field instead of my email address:
FROM me@thisbox instead of FROM bfootdav@bellsouth.net

So what I'm asking is how do I get exim to use my email address
(bfootdav@bellsouth.net) on outgoing mail but not on local mail?

Thanks
David Bellows