How to send mail to localhost using an address other than 127.0.0.1 (loopback interface)

Issue

I need to use an interface other than loopback to send mail.

[root@myserver ~]hostname myserver

[root@myserver ~]cat /etc/hosts
127.0.0.1        localhost.localdomain localhost
::1              localhost6.localdomain6 localhost6
192.168.135.111   myserver

[root@myserver ~]ifconfig
eth0      Link encap:Ethernet  HWaddr ************  
          inet addr:192.168.135.201  Bcast:192.168.135.255  Mask:255.255.255.0