A wet-press arrangement. The flexible press jacket of a shoe press roll removes the web to be dewatered in a first press nip directly from the wire on which the web has been formed. The web then passes, together with the press jacket, through a second press nip which is developed as a felted, lengthened press nip. The web then passes through a third press nip where it is transferred from the smooth outer surface of the press jacket onto the smooth outer surface of a press roll. The web then travels, together with the latter roll, through a fourth press nip, which again is developed as a felted, lengthened press nip. Following that, the web still follows the press roll up to a place of web removal.