There are constraints on pricing congestible facilities. First, if heterogeneous users are observationally indistinguishable, then congestion charges must be anonymous. Second, the time variation of congestion charges may be constrained. Do these constraints undermine the feasibility of marginal cost pricing, and hence the applicability of the first-best theory of congestible facilities? We show that if heterogeneous users behave identically when using the congestible facility and if the time variation of congestion charges is unconstrained, then marginal cost pricing is feasible with anonymous congestion charges. If, however, the time variation of congestion charges is constrained, optimal pricing with anonymous congestion charges entails Ramsey pricing.