A lighting device may include a light source and a reflective optical element. The reflective optical element may have a reflective internal surface that defines a cavity. The internal surface may include longitudinal undulations. The internal surface may be faceted or non-faceted. The light source may be at least partially disposed in the cavity. The shape profile of the internal reflective surface in any plane containing the surface's symmetry axis may be non-paraboloidal and may exhibit undulations running along its length. The reflective optical element may be a monolithic structure and may be a beam-shaping reflector that generates a light beam that, in comparison with a paraboloidal reflector having the same hole size, aperture size, and light source, is relatively fainter at small off-axis angles, brighter at mid-range off-axis angles, and fainter at large off-axis angles than a light beam generated by the paraboloidal reflector. Related methods are provided.