A tissue papermaking machine is described, comprising a wet section and a press section comprising a single press with first and second press elements forming a press nip, and with a press felt running through the press nip in contact with the formed fiber web, whereby the second press element is arranged inside the loop of the press and felt, and a smooth belt runs through the press nip in contact with the formed fiber web, whereby the first press element is arranged inside the loop of the belt, and a transfer roll arranged inside the loop of the belt forming a transfer nip with a drying surface, whereby the smooth belt carries the fiber web between the press nip and the transfer nip. A pre-dewatering device is arranged upstream of the press to dewater the fiber web to a dry content of 15-30%. Associated methods are also provided.