Machine and process for the production of a tissue web that includes a drying cylinder and a press shoe arrangement. The press shoe arrangement and the drying cylinder are arranged to form a nip with lateral edge areas. A plurality of contact pressing elements are arranged to exert pressing pressures across the nip, a measuring device is structured and arranged to measure pressing pressures resulting in at least the lateral edge areas, and at least one of a control and regulating device is structured and arranged to locally adjust the pressing pressures in the lateral edge areas by adjusting pressing pressures exerted by contact pressing elements assigned to the lateral edge areas. The instant abstract is neither intended to define the invention disclosed in this specification nor intended to limit the scope of the invention in any way.