Ensuring secure information ow within programs in the context of multiple sensitivity levels has been widely studied. Especially noteworthy is Denning's work in secure ow analysis and the lattice model [6][7]. Until now, however, the soundness of Denning's analysis has not been established satisfactorily. Weformulate Denning's approach as a type system and present a notion of soundness for the system that can be viewed as a form of noninterference. Soundness is established by proving, with respect to a standard programming language semantics, that all well-typed programs have this noninterference property.