A clutch cover assembly 3 having a disk-shaped clutch cover 4, an annular pressure plate 5, a cone spring 6, and a diaphragm spring 7. The pressure plate 5 is disposed in the clutch cover 4 and has a pressing surface 5a. The cone spring 6 is disposed on the opposite side of the pressure plate 5 in the clutch cover 4, and has its radial inner end supported on the clutch cover and its radial outer end biasing the pressure plate 5. Within the clutch cover, a hardened support member coupled to the cover is provided to engage at least one inner portion of the cone spring 6 in order to minimize wear associated with engagement with the spring 6 as it moves in response to movement of the pressure plate 5. The hardened support member is provided in the present invention is a number of forms. In one embodiment the hardened support member is integrally formed with the clutch cover 4. In another embodiment the hardened support member is a ring 10 formed with a lip 10a which engages a displaceable end of the cone spring 6.