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In packet audio applications, packets are buffered at a receiving site and their playout delayed in order to compensate for variable network delays. In this paper, we consider the problem of adaptively adjusting the playout delay in order to keep this delay as small as possible, while at the same time avoiding excessive “loss” due to the arrival of packets at the receiver after their playout time has already passed. The contributions of this paper are twofold. First, given a trace of packet audio receptions at a receiver, we present efficient algorithms for computing a bound on the achievable performance of any playout delay adjustment algorithm. More precisely, we compute upper and lower bounds (which are shown to be tight for the range of loss and delay values of interest) on the optimum (minimum) average playout delay for a given number of packet losses (due to late arrivals) at the receiver for that trace …