A press device for draining and/or smoothing, or shaping the surface and controlling the sheet structure of fibrous pulp webs with a surface weight of under 100 g/m2, such as the fibrous pulp webs used to make graphic papers. The device has a press area which includes at least one press nip through which, during operation, the fibrous pulp web is fed at a velocity of at least 1200 m/min, under simultaneous impingement by pressure. The press area includes at least two press zones subsequent to one another. The device is further characterized by a K value of at least 2.5 kPa·s·m. This K value is the product of L1 and Itot. L1 is the length of the first press zone, measured along the direction in which the web runs, and Itot is the total press impulse operating on the fibrous pulp web in the entire press area.