How to allow outgoing mail to certain domains with exim4?

[Robert Rothenberg <robrwo@gmail.com>]

I would like to configure exim4 to allow outgoing mail to certain domains.
I've been unable to figure out how to do so from the manual or using the
dpkg-reconfigure utility: messages are bounced back with the error that mail
to remote domains is not supported.

I use a laptop and regularly switch between several networks, so configuring
it to relay to my ISPs outgoing server is not an option (though I've not
been able to get that to work either).

Thanks,
Rob