We present a novel inference algorithm for a type system featuring subtyping and usage (annotation) polymorphism. This algorithm infers simply-polymorphic types rather than the constrained-polymorphic types usual in such a setting; it achieves this by means of constraint approximation. The algorithm is motivated by practical considerations and experience of a previous system, and has been implemented in a production compiler with positive results. We believe the algorithm may well have applications in settings other than usage-type inference.