We present the first direct bounded wait-free implementation of a replicated register with atomic semantics in a system with an unbounded number of clients and in which up to / servers are subject to Byzantine failures. In a system with n ≥ 4f + i + 1 servers, and in the presence of a single writer, our implementation requires 5 messages from the reader and at most 6 + 2(f - i) messages per correct server per read operation and 2 request and 2 reply messages per server for each write operation. Unlike previous solutions, the number of messages is independent of the number of write operations that are concurrent with a read operation. For the case of multiple writers, a read operation requires 5 messages for the reader and no more than 6 + 2c(f - i) reply messages per correct server, where c is the number of writers that execute concurrently with the read operations, and a write operation requires 4 request and 4 reply messages per server. The message requirements of our wait-free implementations are considerably better in the worst case than those of the best known non wait-free implementations. If there is a bound on the number of writers, the total number of messages sent by a server is linear in the number of read operations, so faulty servers that send too many messages will be detected as faulty. This implementation does not rule out the possibility that a reader receives and discards many delayed messages in a read operation, so it is bounded only in an amortized sense. We describe a bounded solution in which a read operation will not receive more than a constant number of messages from a server without detecting the failure of the server. No other solution is bounded - in an amortized sense or otherwise.