Spectral power distribution of trichromatic clusters of light-emitting diodes (LEDs) was optimized for rendering the highest number of colors with a perceptually noticeable gain in chroma (color saturation) out of 1269 Munsell samples. The basic tradeoffs of the number of colors rendered with increased saturation with the number of colors rendered with high fidelity and with luminous efficacy of radiation were established. High-saturation RGB clusters composed of commercially available AlGaInP and InGaN LEDs were modeled for a standard set of correlated color temperatures and the stability of the color saturation ability of the clusters against the drift of peak wavelengths was investigated.