When a database is defined as views over autonomous sources, inconsistencies with respect to global integrity constraints are to be expected. This paper investigates the possibility of using a technique known as simplification of integrity constraints in order to maintain, in an incremental way, a correction table of virtual updates which, if executed, would restore consistency. Access to global data is then made through auxiliary views that take the table into account. This structure is relevant for a service that draws upon external data sources over which it has no write permission. The approach employs assumptions about local source consistency as well as cross-source hypotheses whenever possible.