We consider the design of regulatory policy when the regulator is imperfectly informed about both the firm's cost function and the demand function it faces. To some extent, the optimal policy is the natural "combination" of the policies when there is uncertainty about demand alone or cost alone. But important qualitative differences also exist. For example, prices may optimally be set below marginal cost when there is uncertainty about both cost and demand, although prices will never fall below marginal cost when there is only a single source of uncertainty , whether it pertains to cost or demand.