Methods and systems are provided for efficient handover of a media session between heterogeneous Internet Protocol (IP) networks. A mobile device with Internet access can operate a software program to communicate with a corresponding node. The corresponding node may access the Internet through a firewall which may include Network Address Translation (NAT)-routing functionality. The mobile device establishes a media session with a corresponding node via the transmission of a first media stream and receipt of a second media stream, and a media-control channel can optionally be implemented. The mobile device can acquire Internet access through a second IP address, and packets routed between the second IP address and the Internet may traverse a firewall. The mobile device can evaluate a set of network parameters at the second IP address from a stored Local Area Network (LAN) profile. A software routine can (i) evaluate that handover of the media session from the first IP address to the second IP address is preferred and (ii) select an efficient handover procedure according to handover procedure rules.