A plumbing fixture having a valve supplying water under pressure to an output and a hose outlet having an intake end has a vented backflow preventer having a housing separate from the valve and having an inlet port connected to the valve output and an outlet port connected to the hose intake end. A lower check valve in the housing has a lower seat, an upper seat, and a valve body of density greater than water movable between a lower position sitting on and blocking the lower seat and an upper position sitting on and blocking the upper seat. The housing is formed with an inlet passage leading from the inlet port to the lower seat and an outlet passage leading from between the seats to the outlet port. An upper check valve in the housing above the lower check valve has an upper seat above the lower-valve upper seat and a valve body of a density less than water and movable between an upper position sitting on and blocking the upper-valve upper seat and an upper position clear thereof. The housing is formed with an externally open vent opening into the upper check valve above the upper seat thereof.