A broadband light source includes a phosphor layer excited by light from multiple LEDs. A dichroic reflector reflects light from the LEDs onto the phosphor layer. First and second LEDs are responsible for first and second broadband portions respectively of a broadband output light of the source, each such broadband portion being broadband and nominally white. The device components are configured and arranged so that the first and second broadband light portions have different CIE color coordinates. These portions combine to yield a resultant color for the overall broadband light output of the source, which resultant color is a func tion of the relative amounts of the first and second broadband light portions. An open-loop or closed-loop controller can independently drive the LEDs to provide a desired mix of the broadband light portions so that the overall broadband light output has a color in a desired design space.