In this paper we describe the spatial access method z-ordering and its application in the context of the research project GODOT, which is based on the commercial object-oriented database system ObjectStore. After identifying a range of spatial predicates, we show that the intersection join is of crucial importance for spatial joins. Next, we propose an efficient method for query processing, which takes advantage of z-ordering and uses the conventional indexing mechanisms offered in current database systems (e.g., relational and object-oriented). Furthermore, we show how these concepts are realized in the three-way object-oriented GODOT data model. Finally, we present a general union algorithm for geometric objects represented by their z-val...