A dimmable, light-emitting diode (LED) power supply adapted to provide a direct current (DC), constant current (“constant current source”) from a conventional, phase-controlled 120 VAC, 60 Hz power source is disclosed. The constant current source of the present invention utilizes two processes to control dimming. In a first process, the phase angle of the input voltage is used to control the duty cycle of a line frequency pulse width modulation (PWM). In a second process, a proportional-current limit adjustment is used to control the average current to the LED during the ON time of the line frequency by PWM. As a result, at relatively low phase angles, peak currents can be lowered, reducing flicker and improving the audible noise levels generated by the circuit.