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This paper clarifies issues debated by A. C. Pigou and Frank Knight about correcting inefficient use of congestible resources, focusing for concreteness on their original example of road congestion. Instead of government‐imposed Pigouvian access fees, Knight favoured access fees set by private toll‐setters. We consider the case of n≥2 congestible roads and an uncongestible road of arbitrary speed. Knight argued that in the case of a single congestible road, a private toll‐setter would always choose the toll that Pigou recommended, hence the allocation would minimize aggregate commute time without government meddling. We find instead that two or more toll‐setters would never choose Pigouvian tolls except in the special case of a sufficiently fast uncongestible road. Moreover, for uncongestible roads of slower speed, the allocation of motorists under Knight's proposal is almost never efficient. Whenever it is inefficient, motorists are strictly worse off when they pay tolls set by private firms instead of paying government‐imposed tolls, and aggregate toll revenue is also lower. Nevertheless, if the private sector does set tolls, then the full cost to motorists can be limited if the government provides an uncongestible alternative, such as a train, to offer potential competition along the same route.