An illumination module includes a color conversion cavity with multiple interior surfaces, such as sidewalls and an output window. A shaped reflector is disposed above a mounting board upon which are mounted LEDs. The shaped reflector includes a first plurality of reflective surfaces that preferentially direct light emitted from a first LED to a first interior surface of the color conversion cavity and a second plurality of reflective surfaces that preferentially direct light emitted from a second LED to a second interior surface. The illumination module may further include a second color conversion cavity.