An LED illumination system includes control circuitry and first, second and third colored LEDs. The control circuitry sequentially drives the first, second and third colored LEDs in a color cycle frame with relative duty cycles having a known relationship that achieves a color balance. The control circuitry also operates to introduce at least one spoke period in the color cycle frame, during which the first, second and third LEDs are driven in a manner that is controlled to provide brightness adjusting light that matches the color balance achieved by the relative duty cycles of the first, second and third LEDs during sequential driving thereof.