A reflector for a light source, such as an LED, is provided with a shape which efficiently collects and directs energy to an illumined surface whereby almost 100% of the light is collected and distributed into a designer composite beam. The shape in one embodiment is comprised of three zones beginning with a parabolic surface of revolution at the base of the reflector, followed by a transition orstraight conic zone and ending with an elliptical zone. In another embodiment the reflector shape is determined according to a transfer function which allows for arbitrary designer control of the reflected rays at each point on the reflector, which when combined with direct radiation from the source, results in a designer controlled composite beam or illumination. The device is more than 90% energy efficient and allows replacement of higher power, less energy efficient light sources with no loss in illumination intensity.