The invention is directed to a press system of a paper machine for making tissue, including a crepe drying cylinder, a press roll with a smooth surface, an extended-shoe press unit, and a press roll fashioned as a suction roll or grooved roll. A first press gap is formed by the press roll with a smooth surface and the press roll designed as a suction roll or grooved roll. A water collection tub is coordinated with the suction roll or grooved roll. A second gap is formed between the press roll with the smooth surface and the extended-shoe press unit after which the felt leaves the periphery of the press roll with the smooth surface. Following thereafter, a third press gap is provided between the press roll with the smooth surface and the crepe drying cylinder. The felt does not pass through the third press gap.