>
> is there a way to force Exim to use a given local IP-Address for outgoing
> TCP-connects in favour of another?
>
> I'm talking about a feature like "-I" in the ping command.
You need the 'interface' option on your SMTP transport.
http://www.exim.org/exim-html-4.30/doc/html/spec_30.html#IX2087
Peter