Atomic broadcast primitives 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 which, based on optimistic assumptions about the communication system, reduces the average delay for message delivery. In this paper, we develop this idea further and present a replicated database architecture that employs the new atomic broadcast primitive in such a way that the coordination phase of the atomic broadcast is fully overlapped with the execution of transactions, providing high performance without relaxing transaction correctness.