A printing unit having a press unit is disclosed. Damping solution is applied to a form cylinder by way of direct damping-solution supply via a damping unit in such a way that a damping-solution applicator roll which is set away from an ink distributor roll and is driven by way of friction by the form cylinder rolls only on the form cylinder and thus applies the damping solution to the form cylinder only directly via the damping-solution applicator roll. In the event of indirect damping-solution supply in which the damping-solution applicator roll rolls exclusively on the ink distributor roll and is driven by way of friction by the ink distributor roll, in order to switch over to direct damping-solution supply, the damping-solution applicator roll is set away from the ink distributor roll more quickly than the damping unit, and thus the damping-solution applicator roll, is set against the form cylinder.