of completely smooth or closed roll surfaces and then to the felted press nip iii which is formed again by a shoe press has also proven particularly favorable press felt 18 is preferably formed of a relatively fine fabric so that the paper web 4 is marked relatively little by the press felt 18 at the last press nip iv if such a nip is present in other words the bottom side of the paper web 4 remains relatively smooth upon contact with the press felt 18 the embodiment shown in fig2 is similar to that shown in fig1 again there is a wire section with the moving wire 1 the wire suction roll 2 the deflection roll 3 and the paper web 4 shown in dashed line which is carried on the wire 1 a first press felt 5 conducts the paper web 4 through a first press nip i between the first and second press rolls 9 and 10 roll 9 is a press roll with a smooth i e closed outer surface and not a shoe press as in fig1 alternatively the outer surface of the first press roll 9 can also be provided with fine recesses for instance circumferential grooves for the temporary storage of water the remaining structure of the press is also very similar to that shown in.