Embodiments of the present invention provide separate optical devices operable to couple to a separate LED, the separate optical device comprising an entrance surface to receive light from a separate LED when the separate optical device is coupled to the separate LED, an exit surface opposite from and a distance from the entrance surface and a set of sidewalls. The exit surface has at least a minimum area necessary to conserve brightness for a desired half-angle of light projected from the separate optical device. Furthermore, each sidewall is positioned and shaped so that at least a majority of rays having a straight transmission path from the entrance surface to that sidewall reflect to the exit surface with an angle of incidence at the exit surface at less than or equal to a critical angle at the exit surface.