This paper offers two ways to decentralize the constrained-efficient allocation of the Lagos–Wright (2005) pure currency economy. The first way has divisible money, take-it-or-leave-it offers by buyers, and a transfer scheme financed by money creation. If agents are sufficiently patient, the first best is achieved for finite money growth rates. If agents are impatient, the equilibrium allocation approaches the constrained-efficient allocation asymptotically as the money growth rate tends to infinity. The second way has indivisible money, take-it-or-leave-it offers by buyers, and no government intervention. We discuss the strict implementation of constrained-efficient allocations and the applicability of our scheme to economies with Lucas trees, endogenous participation, match-specific heterogeneity, and sequential competitive markets.