A wear adjuster for a brake caliper of a disk brake of a rail vehicle, having a) a helical gearing which has a threaded spindle and a nut to be screwed thereon as the screw connection elements, one of the screw connection elements and an adjusting element being rotatable in a first wear adjuster housing to rotatingly drive the screw connection element in the wear adjusting direction and the other screw connection element being non-rotatably mounted in a second wear adjuster housing, b) a wrap spring freewheeling mechanism which is blocked in a direction of rotation of the rotatable screw connection element against a wear adjustment and which is freewheeling in the opposite direction of rotation, the wrap spring freewheeling mechanism coupling the rotatable screw connection element to a rotationally fixed element. The rotationally fixed element is formed directly by the first wear adjuster housing.