Adapted packet speech interpolation (APSI) is presented as an evolution of digital speech interpolation (DSI) techniques. The inherent overload penalties of DSI are mitigated by the use of an overload strategy which distributes the penalties uniformly across all active speech sources. A novel use of linear delta modulation (LDM) allows the system to re‐encode the input sources at various rates depending upon the total offered load to the system. The subjective performance of hardware is discussed. Two models of silence and talk‐spurt behaviour (called activity) of speech are presented: an analytic model for single speakers obtained by the application of renewal theory, and a simulation model obtained from the analytic model.