A first telephony device sets up a first communication channel through an Internet protocol (IP) network for conducting an IP based telephony communication with a second telephony device. The first communication channel includes one or more media relays. The first telephony device then begins to conduct the telephony communication with the second telephony device over the first communication channel. While the initial stages of the telephony communication are ongoing, the first telephony device sets up a second communication channel with the second telephony device that does not utilize media relays. The telephony communication is then switched to the second communication channel. Proceeding in this fashion ensures that a communication channel can be rapidly established between the first and second telephony devices so that the telephony communication can quickly commence.