Byzantine quorum systems  enhance the availability and efficiency of fault-tolerant replicated services when servers may suffer Byzantine failures. An important limitation of Byzantine quorum systems is their dependence on a static threshold limit on the number of server faults. The correctness of the system is only guaranteed if the actual number of faults is lower than the threshold at all times. However, a threshold chosen for the worst case wastes expensive replication in the common situation where the number of faults averages well below the worst case. In this paper, we present protocols for dynamically raising and lowering the resilience threshold of a quorum-based Byzantine fault-tolerant data service in response to current information on the number of server failures. Using such protocols, a system can operate in an efficient low-threshold mode with relatively small quorums in the absence of faults, increasing and decreasing the quorum size (and thus the tolerance) as faults appear and are dealt with, respectively.