Singleton arc consistency (SAC) is a local consistency that enhances the pruning capability of arc consistency by ensuring that the network can be made arc consistent after any assignment of a value to a variable. While some algorithms have been proposed in the literature to enforce SAC, a more in-depth theoretical analysis of this local consistency has never been published. In this paper, we give a lower bound to the time complexity of enforcing SAC, and we propose an algorithm that achieves this complexity, thus being optimal. We characterize some properties of SAC which are unusual for a local consistency. Based on some of these properties, we extend SAC to a more powerful local consistency that we compare to the existing local consistencies.