It has already been reported that the CAN protocol produces data inconsistencies in some scenarios that violate the Atomic Broadcast properties. It has been proposed a set of higher level protocols to achieve Atomic Broadcast on CAN based systems. This approach causes considerable overhead. We propose a more efficient solution through small modifications to CAN. Our first proposal of modified protocol is called MinorCAN. Unfortunately we have identified new inconsistency scenarios in which both CAN, MinorCAN and the mentioned higher level protocols still violate the Atomic Broadcast properties. Inspired in the MinorCAN ideas we propose a protocol, called MajorCAN, that really implements Atomic Broadcast.