Integrity checking is aimed at efficiently determining whether the state of the information base is consistent after the application of a set of structural events. One possible way to achieve efficiency is to consider only the relevant instances that may violate an integrity constraint instead of the whole population of the information base. This is the approach we follow in this paper to automatically check the integrity constraints defined in a UML conceptual schema. Since the method we propose uses only the standard elements of the conceptual schema to process the constraints, its efficiency improvement can benefit any implementation of the schema regardless the technology used.