A cover for rest supports such as pillow cases, seat cushions, headrests, armrests, bedding and pet bedding is disclosed with layered secure spare flaps. A plurality of spare flaps are attached in respective layers to the cover at an end of each flap and another end is successively folded around the cover and secured thereto to provide additional unused resting surfaces for a person or an animal. The spare flaps therefore provide multiple fresh resting surfaces between launderings. Embodied flaps may also be disposably detached from the cover to preclude launderings altogether. The layered flaps may include use indicia and be to secured to each other and a rest support cover via a fastener on a flap and a complementary fastener disposed respectively on the cover. Disclosed fasteners include thin magnets, hook and loop, grommet and tie, button and hole and ganged hole and post pairs and the like.
