White LED spectra for general lighting should be designed for high luminous efficacy as well as good color rendering. Multi-chip and phosphor-type white LED models were analyzed by simulation on their color characteristics and luminous efficacy of radiation, compared with those of conventional light sources for general lighting. Color rendering characteristics were evaluated based on the CIE Color Rendering Index (CRI), using not only Ra but also the special color rendering indices Ri as well as the CIELAB color difference ΔE*ab for the 14 color samples defined in CIE 13.3. Several models of 3-chip and 4-chip white LEDs as well as phosphor-type LEDs are optimized for various parameters, and some guidance is given for designing these white LEDs. The simulation analysis also demonstrated several problems with the current CIE Color Rendering Index (CRI), and the need for improvements is discussed.