The authors build on previous experience in the optimization of white light sources based on combinations of known narrow-band spectra. The authors extend these concepts by using synthetic (mathematically generated) four-band spectra to study the prospects for the spectral design of future optimal light sources. The optimization is based on achieving a trade-off of the color rendering properties against the luminous efficacy of the radiation, using the differential evolution (DE) algorithm. It is shown that this trade-off is controllable through the choice of the optimization parameters, specifically the choice of terms in the optimization fitness function. Depending on the choice of the shapes for the synthetic spectral bands, the results are comparable with those achieved in earlier work on the optimization of four-band light-emitting diode (LED) spectra. However, the range of color temperatures achieved in the present study is considerably wider than was previously found for optimum four-band LED mixtures.