A packetized speech multiplexer differs from a circuit-switched TASI system in that the presence of a packet buffer allows a tradeoff where the TASI advantage can be increased at a cost in packet delay. This tradeoff is investigated via a simulation. Results are presented to show the relations between TASI advantage and delay, for both an average delay criterion and a maximum delay criterion. It is shown that, particularly for the case where small numbers of talkers are multiplexed, the packetized system offers significant improvements in TASI advantage over the conventional circuit-switched multiplexer, at modest costs in packet delay.