If a -field is sufficient for a family of probability measures defined on a -field then there exist regular determinations of the conditional probability of P, given , which are independent of the special measure , provided that is -regular. A counterexample shows that the -regularity of cannot be replaced by the assumption that each is approximable by a fixed compact system. In particular if a -field is sufficient for a family of probability measures defined on a separable -field and if each admits a regular conditional probability, given , a common regular conditional probability, given , need not exist.