A method for conveying sheets through a printing machine and an apparatus for conveying the sheets permit adaptation of a sheet brake to various sheet thicknesses by reducing a speed of the sheets in the direction of advance by bringing the sheets individually one after another into contact with at least one suction element moved in the direction of advance, and by holding each sheet by the action of a suction apparatus on the suction element along a conveying section, dependent upon the sheet thickness, the suction action of the suction element along the conveying section is changed locally.