A substrate holder is described which has a movable plate elastically mounted inside a main body. With the substrate holder, a polishing operation can be performed in two basic operation modes corresponding to two different vertical end positions of the movable plate. In a first (downward) mode the movable plate stays in mechanical contact with the substrate whereas in a second (upward) mode an air cushion is generated in a chamber between the movable plate and the substrate for pressurizing the substrate onto the polishing pad.