[Exim] Outbound Mail Missing Domain Name

Outbound mail sent locally (from web server or scripts, other programs) seem to
be sent as <user>@machinename without a fully qualified domain name.

I've checked everywhere I can think of to where Exim could be missing the FQDN.

primary_hostname is set correctly, and /etc/hosts appears to be reasonable.

Any ideas on FAQ's on this subject. Again, it's when it's generated by a local
user without -f to force the from address.

Thanks...