>How to make the headers of the messages transfered by Exim _not_ to >mention domainname?
You can't. Not withoug modifying the source code quite extensively.
>For example, I want a message message from foo@the_localdomain to have
>the "To:" header set to "foo" (without the domainname...)
Why not just use the qualify_ options to set the local domain and such? Then
you could still mail "Foo" and it would get deleivered to foo@qualify_domain
