The weak distance between two vertices in a digraph G is the length of a shortest directed path connecting these two vertices. The weak diameter of a digraph G is the longest weak distance among all pairs of vertices in G. We define w(n, d) to be the smallest number of edges a digraph G with n vertices and weak diameter d can have. We determine w(n, d), whenever n is large enough as a function of d. This is joint work with Zoltan Füredi.