A variety of illumination devices for general illumination utilizing solid state light sources (e.g., light-emitting diodes) are disclosed. In general, an illumination device can include multiple light sources that are disposed on a substrate, where at least some of the light sources include a light-emitting diode (LED) and a corresponding inelastic scattering element surrounding, at least in part, the LED. The inelastic scattering elements can have different light emission spectra. The illumination device can further include a light-mixing element adapted to receive light that is output by the light sources, where, during operation of the illumination device, each inelastic scattering element inelastically scatters light emitted from its corresponding LED, and the light-mixing element mixes the light received from the inelastic scattering elements to provide the output light.