Existing Byzantine-resilient replication protocols satisfy two standard correctness criteria, safety and liveness, even in the presence of Byzantine faults. The runtime performance of these protocols is most commonly assessed in the absence of processor faults and is usually good in that case. However, faulty processors can significantly degrade the performance of some protocols, limiting their practical utility in adversarial environments. This paper demonstrates the extent of performance degradation possible in some existing protocols that do satisfy liveness and that do perform well absent Byzantine faults. We propose a new performance-oriented correctness criterion that requires a consistent level of performance, even with Byzantine faults. We present a new Byzantine fault-tolerant replication protocol that meets the new correctness criterion and evaluate its performance in fault-free executions and when under attack.