Embodiments of the present invention are directed toward white light illumination systems (so called “white LEDs”) that comprise a multi-chip excitation source and a phosphor package. In a two-chip source, the two LEDs may be UV-emitting and blue emitting, or blue-emitting and green-emitting. The phosphor package is configured to emit photoluminescence in wavelengths ranging from about 440 nm to about 700 nm upon co-excitation from the first and second radiation sources. The photoluminescence emitted by the phosphors is at least 40 percent of the total power in the white light illumination, and the portion of the total power in the white light illumination contributed by the first and second radiation sources (LEDs) is less than about 60 percent. This ratio can vary in alternative embodiments, and includes 50/50, 60/40, 70/30, and 80/20, respectively. The white light illumination emitted by the system has in one embodiment a color rendering index (CRI) greater than about 90.