In this work, we investigate the routing problems ofminimizing the number ofdistinct transmission mediums or carrier domains for multimedia communications. We consider the problems of two-party connection as well as three-or-more-party connections. By minimizing the number of distinct transmission mediums or carrier domains on the connections, rather than minimizing bandwidth, length or hop counts, the network carriers may achieve higher cost savings on connection provisioning and management. These problems are proven to be NP-hard. Heuristic algorithms are proposed for larger instances ofthe problems and evaluated through simulations.