An apparatus and method for driving a driven unit of a printing press, specifically a printing couple or a folding unit of a rotary web press, is disclosed. A cylinder or roller to be driven is driven by a drive with an interposed transmission. An input element is mounted on a shaft of the cylinder or the roller to be driven and an output element is assigned to the drive co-acting with the input element. A shaft of the drive is carried in at least two bearing locations. The output element is mounted directly to the shaft of the drive such that the output element is located immediately adjacent a bearing location of the shaft of the drive.