Commercial databases support different isolation levels to allow programmers to trade off consistency for a potential gain in performance. The isolation levels are defined in the current ANSI standard, but the definitions are ambiguous and revised definitions proposed to correct the problem are too constrained since they allow only pessimistic (locking) implementations. This paper presents new specifications for the ANSI levels. Our specifications are portable; they apply not only to locking implementations, but also to optimistic and multi-version concurrency control schemes. Furthermore, unlike earlier definitions, our new specifications handle predicates in a correct and flexible manner at all levels.