LED apparatus for illumination toward a preferential side, including a light emitter having at least one LED on a base, a primary lens positioned over the light emitter and having a central axis, and a secondary lens placed with an inner surface surrounding the primary lens. The secondary lens has a base-adjacent lower end defining a main plane substantially perpendicular to the central axis, anda compound outer lens surface with a middle-region reference point defining a reference axis parallel to the central axis. The compound outer lens surface includes (A) a principal perimeter surface centered on the preferential side, the principal perimeter surface (a) projecting to a ridgeline subtending a substantial angle about the central axis, and (b) terminating inwardly at the ridgeline, (B) a middle region containing the reference point and having a concavity thereabout, and (C) a non-principal perimeter surface centered on the non-preferential side and adjoining the middle region and the principal perimeter surface.