The authors showed previously that for each of the varieties B n ( 3 ≤ n > ω ) {{\mathbf {B}}_n}(3 \leq n > \omega ) of pseudocomplemented distributive lattices there exists a natural duality given by a set of p ( n ) + 3 p(n) + 3 binary algebraic relations, where p ( n ) p(n) denotes the number of partitions of n n . This paper improves this result by establishing that an optimal set of n + 3 n + 3 of these relations suffices. This is achieved by the use of "test algebras": it is shown that redundancy among the relations of a duality for a prevariety generated by a finite algebra may be decided by testing the duality on the relations, qua algebras.