A primary optic for a light-emitting diode or device (LED) includes a tilted wedge atop a truncated compound parabolic concentrator (CPC). The CPC includes an input face and a lower exterior surface defined by a tilted parabolic segment rotated about an axis. The bottom end of the lower exterior surface joins the perimeter of the input face. The tilted wedge includes an upper exterior surface above the lower exterior surface, and an interior conical surface surrounded by the lower and the upper exterior surfaces. The upper exterior surface is defined by a tilted straight line rotated about the axis. The interior conical surface is defined by a smooth curve rotated about the axis. The interior conical surface has a vertex located at the axis and within the lower exterior surface. The top ends of the interior conical surface and the upper exterior surface join to define an output aperture.