Abstract: Outerjoins and antijoins are two important classes of joins in database systems. Reordering outerjoins and antijoins with inner joins is challenging because not all the join orders preserve the semantics of the original query. Previous work didn't consider antijoins and was restricted to a limited class of queries. We consider using a conventional bottom-up optmizer to reorder different types of joins. We propose extending each join predicate's eligibility list, which contains all the tables referenced in the predicate. An extended eligibility list (EEL) includes all the tables needed by a predicate to preserve the semantics of the original query. We describe an algorithm that can set up the EELs properly in a bottom-up traversal of the original operator tree. A conventional join optimizer is then modified to check the EELs when generating subplans. Our approach handles antijoin and can resolve many practical issues. It is now being implemented in an upcoming release of IBM's Universal Database Server for Unix, Windows and OS/2.