A property P of algebras in any variety V might be called S-determined if when A has P and A, A' have isomorphic lattices of subalgebras. A' has P; S-sharp if the same conditions imply \(A'=F(A)\) for some automorphism F of V. The authors show that being a pseudocomplemented lattice of finite length is S-determined, and produce two new S-sharp properties of lattices.