A communications system includes a plurality of radios that form a CSMA wireless communications network to communicate none-packetized digital voice with each other. Each radio is operative for dividing the period following the end of a received transmission into a sequence of time slots, each having a duration at least equal to an effective end-to-end traffic latency. In each time slot, the radio decides randomly with probability p whether to start transmitting on the channel in that slot, provided that a new transmission has not been detected on the channel prior to the start of the slot.