[Exim] Local MX / DNS.

One thing that has never struck me.

Ponder i want to run a domain on a local net without a DNS, how on earth
would i designate a MX? Answer is most likely " i cant". So, i assume i will
have to send mails to the FQDN of the mailserver, so it finds itself in
/etc/hosts? Or is there an answer i am missing? (Customer refuses to set up
a DNS for the local parts of the network)