The following article is available as a preprint from the first-named author, and will also be available as soon as possible by ftp. Constructive Complete Distributivity II Robert Rosebrugh* and R.J. Wood** Abstract A complete lattice, L, is constructively completely distributive, (CCD)(L), if the sup map defined on down-closed subobjects has a left adjoint. It was known that in boolean toposes (CCD)(L) is equivalent to (CCD)(L^op). We show here that the latter property for all L (sufficiently, for Omega) characterizes boolean toposes. Along the way we also consider Heyting algebras satisfying the `infinite DeMorgan Law' i.e. negation has a right adjoint. We show that a topos is boolean iff Omega satisfies this law. *<RROSEBRUGH@MTA.BITNET> **<rjwood@cs.dal.ca>