A display uses x illuminator systems to produce x primary colors and y overlap colors, which are combinations of primary colors, to illuminate a spatial light modulator in a display system. A first set of n duty cycles for the x primary colors over a frame is provided, wherein the display system can select any one of the duty cycles to produce a desired white point. A second set of n duty cycles of x+y colors over a frame corresponding to the first set of duty cycles is determined, where the second set of duty cycles are generated responsive to a specified desired allocation of the frame to the y overlap colors, such that each of the overlap colors can be displayed from a dark shade to a bright shade while maintaining a constant color point.