Abstract: A stacking panel covering for an architectural opening includes a headrail and a plurality of suspended from the headrail. The panels form an overlapped stack at one end of the headrail when the stacking panel covering is opened, and cover the architectural opening when the stacking panel covering is closed. The panels are piggybacked on those adjacent thereto, so that they stack, one behind the next, when the stacking panel covering is opened, and so that each pulls the next adjacent thereto as the stacking panel covering is being closed. The panels themselves may be planar, or convexly curved in a horizontal direction and substantially straight in a vertical direction.