A remembered set for a memory heap region in a garbage-collected computer system is modified to classify reference locations stored therein by the heap region from which the references originate so that the number of references originating from a given region can be easily determined. If the number of remembered set entries for references from a second region to a first region reaches a predetermined threshold, the second region is constrained so that it will be collected at the same time as, or before, the first region. Then, all entries in the remembered set associated with the first region for references from the second region to the first region can be deleted, and no such entries need be entered in the future thereby reducing the size of that remembered set and the time required to scan it.