An LED conversion system is used in connection with a recessed light housing mounted in a ceiling. The housing has a can with apertures through it and an electrical socket mounted inside. An electrical source of AC current is connected to the socket. A lamp fitting into the can has a shell with a flat or domed top and a plurality of LEDs. Two bolts and nuts attach the shell to the can. The first end of each bolt is hook-shaped to hook into the apertures. The second end has a thread. Each nut has a head and an elongated portion with an internal thread. A power supply is converts AC to DC current to power the LEDs. The power supply has an enclosure and a circuit board. An electrical plug connects the power supply to the socket. A plurality of conductors connects the power supply to the LEDs. An optional ocular plate can be a diffuser, a filter, or a fresnel lens.