Gmail - Send using a domain alias without the "On Behalf Of" message

I recently set up a second domain as an alias in my google apps account.  The setup was easy, except that when anyone received an email in outlook it would have the email alias "On Behalf Of" the non-alias account.  Most people stated that you just need to pay for the premium subscription, but this is NOT true.  The final solution that worked is to set up the alias to send through a "different" smtp server that is really just the original smtp server.

Directions can be found in this post:
http://webapps.stackexchange.com/questions/196/how-do-i-get-rid-of-on-behalf-of-from-my-sent-gmail-messages