Byzantine-Fault-Tolerant (BFT) state machine replication is an appealing technique to tolerate arbitrary failures. However, Byzantine agreement incurs a fundamental trade-off between being fast (i.e. optimal latency) and achieving optimal resilience (i.e. 2f + b+ 1 replicas, where f is the bound on failures and b the bound on Byzantine failures [9]). Achieving fast Byzantine replication despite f failures requires at least f + b - 2 additional replicas [10, 6, 8]. In this paper we show, perhaps surprisingly, that fast Byzantine agreement despite f failures is practically attainable using only b - 1 additional replicas, which is independent of the number of crashes tolerated. This makes our approach particularly appealing for systems that must tolerate many crashes (large f) and few Byzantine faults (small b). The core principle of our approach is to have replicas agree on a quorum of responsive replicas before agreeing on requests. This is key to circumventing the resilience lower bound of fast Byzantine agreement [6]. © 2010 IEEE.