Disclosed is a cleaning device for cleaning washware. The cleaning device may be a conveyor dishwasher. The cleaning device has at least one cleaning chamber and at least one transportation device. The transportation device transports the washware through the cleaning chamber in a transportation direction. The cleaning device has at least one final-rinse nozzle system for applying at least one final-rinse fluid, in particular fresh water, to the washware. The final-rinse nozzle system has at least two final-rinse nozzle units which are arranged in different positions transverse to the transportation direction. The final-rinse nozzle units can be switched independently of one another in order to apply the final-rinse fluid to the washware in the different positions independently of one another.