A downlight fixture includes an optic housing, a light-emitting diode (LED) array, and a lens-less reflector. The LED array emits directional light rays in a downward direction towards an illuminated target. The reflector is mounted within the optic housing and adjacent to the LED array. The reflector has a hyperbolic wall continuously extending between a narrow neck and a wide bell. The light rays are spread into a light beam within the reflector upon making contact solely with the hyperbolic wall.