A diverter valve for a faucet directs water to either the faucet spout or a spray nozzle. The faucet assembly of the present invention includes a shuttle chamber from which water may access either of two outlet paths. A poppet valve selectively enables water flow from the shuttle chamber to the outlet path leading to the faucet spout whenever the water pressure in the outlet path leading to the spray nozzle is greater than or equal to the pressure in the shuttle chamber. When the spray nozzle is actuated, pressure in the outlet path leading to the nozzle is relieved and the poppet valve closes off the outlet path leading to the faucet spout. A bypass channel is provided between the shuttle chamber and the outlet path leading to the spray nozzle, thereby allowing water to flow through the nozzle while it is actuated. A precision sized orifice in the bypass channel maintains the pressure differential acting on the poppet valve so that flow to the faucet spout remains cut off while the spray nozzle is actuated.