We consider policies for deciding which cells will be lost or dropped when losses occur at a finite buffer ATM node. The performance criteria of interest % particularly for voice traffiç are the delay of transmitted (non-lost) cells, the jitter (or variability in the delay of transmitted cells), and the burstiness of lost cells. We analyze the performance tradeoffs for various cell dropping policies. We show the usual the «rear dropping» in which cells that arrive to a full buffer are lost stochastically maximizes delay, while «front dropping,» in which cells at the front of the buffer are lost, stochastically minimizes delay. On the other hand, rear dropping stochastically minimizes the jitter. We also propose policies that have both stochastically smaller delay and less lost cell burstiness in a stochastic majorization sense than the rear dropping policy.