SIP: Fax Disconnects Immediately After Call Connects

We had this problem where when a person faxed outside the company, the fax would connect to the other end fax, but it will immediately disconnect.  This was interesting to say the least, but what we found was that there was a codec mismatch happening.  We actually had to rearrange the order our CUCM would present codecs for matching so that the carrier would accept them properly.  You can see below where the call would connect (with the 200 ok message), but we would immediately get a bye message disconnecting the call.  Again, codec mismatch with the carrier.
Below is from TranslatorX.  I have cut out from the bigger picture the important pieces of this diagram.