In this paper we present two protocols for asynchronous Byzantine quorum systems (BQS) built on top of reliable channels-one for self-verifying data and the other for any data. Our protocols tolerate f Byzantine failures with f fewer servers than existing solutions by eliminating nonessential work in the write protocol and by using read and write quorums of different sizes. Since engineering a reliable network layer on an unreliable network is difficult, two other possibilities must be explored. The first is to strengthen the model by allowing synchronous networks that use time-outs to identify failed links or machines. We consider running synchronous and asynchronous Byzantine quorum protocols over synchronous networks and conclude that, surprisingly, “self-timing” asynchronous Byzantine protocols may offer significant advantages for many synchronous networks when network time-outs are long. We show how to extend an existing Byzantine quorum protocol to eliminate its dependency on reliable networking and to handle message loss and retransmission explicitly.