Geo-replication poses an inherent trade-off between low latency, high availability and strong consistency. While NoSQL databases favor low latency and high availability, relaxing consistency, more recent cloud databases favor strong consistency and ease of programming, while still providing high scalability. In this paper, we present Antidote SQL, a database system that allows application developers to relax SQL consistency when possible. Unlike NoSQL databases, our approach enforces primary key, foreign key and check SQL constraints even under relaxed consistency, which is sufficient for guaranteeing the correctness of many applications. To this end, we defined concurrency semantics for SQL constraints under relaxed consistency and show how to implement such semantics efficiently. For applications that require strict SQL consistency, Antidote SQL provides support for such semantics at the cost of requiring coordination among replicas.