A self-oscillating flyback converter includes a controller integrated circuit housed in a 3-pin package. A switch control terminal is coupled to the base of an inductor switch that controls the current through a primary inductor of the converter. The controller IC adjusts the on time of the switch such that output current remains constant in constant current mode and output voltage remains constant in constant voltage mode. A signal received on a switch control terminal turns the switch off and provides an indication of the output current when the switch is on. A signal received on a feedback terminal powers the controller IC and provides an indication of the output voltage when the switch is off. The controller IC is grounded through a ground terminal. The flyback converter transitions from critical conduction mode to discontinuous conduction mode at light loads to prevent its efficiency from deteriorating at high switching frequencies.