A device for processing containers with a lip on container support units arranged at regular intervals on a support frame and having at least a container support and a container dish, with the distance from the container support unit to a conveyance plane being changed through variation of the overall height of the container support unit. Also, a method for labeling containers with a support ring, with multiple container support units arranged at regular intervals on the rotating support frame, the container support units having at least a container support and a container dish, with the containers being at least partially clamped between a container support unit and a centering bell during their conveyance through a processing track, and with the distance from a transport plane to the container support unit being varied by changing the overall height of the container support unit according to the size of the containers to be processed.