Methods of producing cellulosic or lignocellulosic materials for use in papermaking include treating a cellulosic or lignocellulosic dry feedstock having a first average molecular weight with ionizing radiation, and controlling the dose of ionizing radiation such that the average molecular weight of the feedstock is reduced to a predetermined level. A method of producing an irradiated paper product includes treating a paper product including a first carbohydrate-containing material having a first molecular weight with ionizing radiation, and controlling the dose of ionizing radiation so as to provide an irradiated paper product with a second carbohydrate-containing material having a second molecular weight higher than the first molecular weight. Pulp and paper products are produced.