A method and apparatus for providing, illustratively, voice data over an asynchronous transfer mode (ATM), Internet Protocol (IP) or other communications network where the voice data is preferentially encoded at a high fidelity level, formed into transport cells or packets, and multiplexed onto a communications channel with, optionally, data traffic. In response to network congestion or buffer over utilization, the voice data is encoded at a medium or low fidelity level to reduce the amount of encoded data necessary to represent the voice data.