We propose a design method for single reflectors that takes into account extended sources with any arbitrary luminance distribution. This method is suitable for non-uniform prescribed illuminance distributions with arbitrary shapes. We use the method of supporting ellipsoids developed by Oliker in conjunction with optimization in order to control the effects of the source extent. Design examples related to street illumination and LED illumination are presented.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.