A printing press having an apparatus for determining the product thickness of a folded product which is fed to folding rolls for making a fold known as the third fold. The apparatus has measuring heads that are arranged on both sides of a folding roll bearing levers. For the purpose of presetting, the product to be folded is introduced slowly between folding rolls. The position of the folding rolls is determined, and a setting signal is generated therefrom and supplied to an actuating motor via a machine presetting means. The actuating motor sets the position of the folding roll levers, such that the folding rolls can be set relative to one another with regard to their mutual spacing, in accordance with the thickness of the folded product.