We identify a large subdomain, D, of quasilinear economies on which any efficient exchange rule will be generically (in the Baire sense) manipulable. For generic economies outside of D, we find rules that are locally non-manipulable. The interior of the set D consists of all economies in which competitive equilibrium would prescribe that all agents consume a positive quantity of money. Since we study quasilinear preferences, this is the domain of primary interest. Our locally non-manipulable rules rely on the existence of traders who are willing to sell all of their cash and absorb the imbalances in the trading of the commodity.