Abstract: A running web which contains moisture is caused to travel through the nip of two squeezing rollers one of which is deformable in that it comprises a stationary carrier and a cylindrical shell which surrounds the carrier and also surrounds a first set of inflatable cushions adjacent the nip and a second set of inflatable cushions opposite the first set. Sensors monitor the moisture content of selected longitudinally extending portions of the web, and the signals which are generated by such sensors are processed by an evaluating circuit and are transmitted to valves which regulate the pressure of pneumatic fluid in the cushions. Each cushion of the second set registers with a cushion of the first set, and the registering cushions can receive fluid from associated sets of valves including a pressure regulating valve which can increase or reduce the pressure of fluid in the respective cushions and a second valve which can shift the admission of fluid from one into the other of the registering valves.