Available-Partition-tolerant (AP) geo-replicated systems trade consistency for availability. They allow replicas to serve clients’ requests without prior synchronization. Potential conflicts due to concurrent operations can then be resolved using a conflict resolution mechanism if operations are commutative and execution is deterministic. However, a Byzantine replica can diverge from deterministic execution of operations and break convergence. In this paper, we introduce ASPAS: As Secure as Possible highly Available System that is a Byzantine resilient AP system. ASPAS follows an optimistic approach to maintain a single round-trip response time. It then allows the detection of Byzantine replicas in the background, i.e., off the critical path of clients requests. Our empirical evaluation of ASPAS in a geo-replicated setting shows that its latency in the normal case is close to that of an AP system, and one order of magnitude better than classical BFT protocols that provide stronger (total ordering) guarantees, unnecessary in AP systems.