This paper presents a new protocol for atomic broadcast in an asynchronous network with a maximal number of Byzantine failures. It guarantees both safety and liveness without making any timing assumptions or using any type of “failure detector.” Under normal circumstances, the protocol runs in an “optimistic mode,” with extremely low message and computational complexity — essentially, just performing a Bracha broadcast for each request. In particular, no potentially expensive public-key cryptographic operations are used. In rare circumstances, the protocol may briefly switch to a “pessimistic mode,” where both the message and computational complexity are significantly higher than in the “optimistic mode,” but are still reasonable.