A container-processing machine includes a rotor with processing positions formed thereon, a transfer station, and a static lifting element used by all the processing positions. Each processing position has a processing head and a container carrier. The lifting element is a static lifting element that is used by all of the processing positions. When the processing position is at the transfer station, the lifting element causes relative motion between a container carrier and a processing head of the processing position. This causes the processing position to transition between receiving and discharge states.