We propose a novel method for designing reflectors with large-size spherical surface sources. The center portion of the reflector is designed using the edge-ray principle, while the rim portion is designed based on the variable-separation mapping method. Step discontinuities are introduced during rim surface construction to control the deviation caused by error in normal vectors, and a feedback modification is adopted to compensate for the illuminance deviation produced by the large size of sources. As an example, a streetlamp with a desired rectangular illuminance distribution on the road is designed using a spherical surface source (10 cm diam) and a compact reflector. It has an illuminance uniformity of 60.2% and utilance of 66.9%, considerably improved from the traditional values of 35 and 40%, respectively.