Some classes of digraphs are reconstructed from the point-deleted subdigraphs for each of which the degree pair of the deleted point is also known. Several infinite families of known counterexamples to the Digraph Reconstruction Conjecture (DRC) turn out to be reconstructible in this sense. A new conjecture concerning reconstruction of digraphs in this sense is proposed and none of the known counterexample pairs to the DRC is a counterexample pair to this new conjecture