Method for starting offset printing press and controlling application of dampening solution and offset printing press

A method for operating an offset printing press having at least one printing unit with an inking unit, a plate cylinder for receiving a printing plate, a blanket cylinder, an impression cylinder and a dampening unit, and for controlling an application of dampening solution from the dampening unit onto the plate cylinder, includes predampening the printing plate. After a printing pressure has beenswitched on between the blanket cylinder and the impression cylinder and after a printing material transport through the offset printing press has been switched on, a supply of dampening solution to the plate cylinder in the printing unit is reduced to a pronounced extent at least once for a short predefined time period, as a result of which an excess of dampening solution produced by the predampening does not accumulate permanently in the inking unit. A printing press for carrying out the method is also provided.