It is well known that, for a congestible facility with a constant long-run average cost, the revenue from the unconstrained optimal toll (set so that each individual faces marginal (social) cost of a use) covers the cost of optimal capacity. This paper investigates under what circumstances the first-best pricing and investment rules apply when time variation of the toll is constrained, and when users differ in unobservable characteristics so that the same toll must be applied to heterogeneous users. Both the bottleneck model and the traditional flow congestion model are considered.