Best CODEC

Trying to do some fancy bridging. Someone calls from a cell phone, the call is forwarded to mt Asterisk box over IAX. Asterisk answers and the user selects something that forwards the call back over IAX to another cell phone. The quality is OK but there is a noticable degrigation as compared to a direct connection.

I connect through exgn.net

[exgn]
type = friend
host = iax.exgn.net
context = inbound
secret = ****
allow = all

Does anyone have any pointers to improve quality. I have lots of bandwidth. Would a SIP connection work better than IAX?