A key is simple if it consists of a single attribute. It is shown that if a relation schema is in third normal form and every key is simple, then it is in projection-join normal form 1992, the ultimate normal form with respect to projections and joins. Furthermore, it is shown that if a relation schema is in Boyce-Codd normal form and some key is simple, then it is in fourth normal form (but not necessarily projection-join normal form). These results give the database designer simple sufficient conditions, defined in terms of functional dependencies alone, that guarantee that the schema being designed is automatically in higher normal forms. © 1992, ACM. All rights reserved.