How to Hide a SIP connection

I'm developing a SIP mobile softphone, customer needs a complete hiding of SIP messages from softphones to SIP servers as VOIP calls are regionally prohibited, however using TLS connection was not sufficient since the message headers are easily recognized as a SIP message. What are the best common alternative? what about openvpn, IPSec tunneling?

Transmitting SIP over TLS means the SIP headers will only be viewable if someone is able to compromise your TLS keys, i.e. it's highly unlikely unless some national security agency is on your case.

What you might be encountering is port 5061 being blocked since it's the default and therefore well known SIP TLS port. To get around that simply use a different port for your SIP TLS connection. As far as anyone viewing the traffic goes if it's not suing port 5061 they won't have any idea that SIP is being used in your TLS stream.

Of course you also need to consider the RTP traffic which is what will carry the audio part of the call once SIP has set it up. There are no standardised ports for RTP but some popular VoIP softswitches do use certain ranges by default. For example Asterisk uses UDP 10,000 to 20,000. To work around that you'd really need to use SRTP but that's going to be harder to set up since not that many SIP user agents and servers support it. It will also be easier to detect for someone watching your traffic since even without knowing the contents the profile of RTP packets would be detectable. Still it's likely to need a sophisticated entity monitoring your traffic to detect a VoIP call using SIP over TLS on a non-standard port and SRTP call amongst the general noise of internet traffic.