Two competing monetary policy prescriptions are analyzed within the context of overlapping generations models. The real-bills prescription is for unfettered private intermediation or central bank operations designed to produce the effects of such intermediation. The quantity-theory prescription, in contrast, is for restrictions on private intermediation designed to separate "money" from credit. Although our models are consistent with quantity-theory predictions about money supply and price-level behavior under these two policy prescriptions, the models imply that the quantity-theory prescription is not Pareto optimal and the real-bills prescription is.