We show that a variety V is congruence distributive if and only if there is some h such that the inclusion \alpha(R\circ R)\subseteq (\alpha R)^k holds in every algebra in V, where juxtaposition denotes intersection, varies among tolerances and varies among U-admissible relations, that is, binary relations which are set-theoretical unions of reflexive and admissible relations. For any fixed h, a Maltsev-type characterization is given for the above inclusion. The results suggest that it might be interesting to study the structure of the set of U-admissible relations on an algebra, as well as identities dealing with such relations.