Atomic Broadcast (all processes deliver the same set of messages in the same order) is a very powerful communication primitive when one is interested in building fault-tolerant distributed systems. Moreover, it has been shown that Atomic Broadcast and Consensus are equivalent problems in asynchronous distributed systems prone to process crash failures. Hence, several Consensus-based Atomic Broadcast protocols have been designed. This paper introduces a new and particularly efficient Consensus-based Atomic Broadcast protocol. The efficiency is obtained by limiting the use of the Consensus subroutine to the cases where asynchrony and crashes prevent processes from obtaining a simple agreement on the message delivery order. The protocol assumes n<2f (where n is the number of processes and f the maximum number of them that can crash). In the most favorable cases, it requires two communication steps for processes to determine a message batch. In the worst case it requires an additional Consensus execution. It is shown that, when n<3f, the protocol can be simplified. It then requires a single communication step in the most favorable cases. This exhibits an interesting tradeoff relating the cost of the protocol with the maximum number of process failures.