We consider a version of Kiyotaki and Wright's monetary search model in which agents can hold arbitrary amounts of divisible money. A continuum of stationary equilibriums, indexed by the aggregate real-money stock, exist with all trading occurring at a single price. There is always a maximum level of the real money stock consistent with existence of such an equilibrium. In the limit as trading becomes faster relative to discounting, any real money stock becomes feasible in such an equilibrium. In contrast to the original Kiyotaki-Wright model, higher equilibrium real money stocks unambiguously correspond to higher welfare.