High-power integrated LEDs usually have a bright square surface. When the rays emitted from them are collected to project a round spot at a very short distance using a rotationally symmetrical reflector, there will be a dark spot in the centre. This problem can be avoided in advanced lighting systems. A discontinuous surface reflector is designed by a simple method based on the three-dimensional form of compound parabolic concentrators. The dark spot is removed, and the uniformity is better.