A cleaning device for cleaning an atomizer, in particular a rotary atomizer, is provided. The cleaning device includes a wet cleaning station having at least one cleaning nozzle for the wet cleaning of the atomizer with a cleaning fluid. The atomizer is introduced into the wet cleaning station in an introduction direction. The cleaning nozzle has a rotatable cleaning trunk for dispensing the cleaning fluid. The cleaning device, in some embodiments, also includes a dry cleaning station. A corresponding operating method is also provided.