We discuss the regulation of a multiproduct monopolist when the firm has private information about cost or demand conditions. The regulator offers the firm a set of prices from which to choose. When there is private information only about costs, the firm should always have a degree of discretion over its pricing policy. When uncertainty concerns demand, whether discretion is desirable depends on how demand elasticities vary with the scale of demands. If a positive demand shock is associated with a reduction in the market elasticity, discretion is good for overall welfare; otherwise it is not.