Atomic broadcast primitives are often proposed as a mechanism to allow fault-tolerant cooperation between sites in a distributed system. Unfortunately, the delay incurred before a message can be delivered makes it difficult to implement high performance, scalable applications on top of atomic broadcast primitives. Recently, a new approach has been proposed for atomic broadcast which, based on optimistic assumptions about the communication system, reduces the average delay for message delivery to the application. In this paper, we develop this idea further and show how applications can take even more advantage of the optimistic assumption by overlapping the coordination phase of the atomic broadcast algorithm with the processing of delivered messages. In particular, we present a replicated database architecture that employs the new atomic broadcast primitive in such a way that communication and transaction processing are fully overlapped, providing high performance without relaxing transaction correctness.