A power supply including a regulation circuit that maintains an approximately constant load current with line voltage. An example circuit includes a switch including first, second and third terminals. The first terminal is coupled or decoupled to the second terminal in response to a control signal received at the third terminal. Voltage sense circuitry is included and is coupled to sense a voltage drop across the switch. The voltage drop is representative of a current in the switch during an on time of the switch. The voltage sense circuitry has a variable current limit threshold that increases between a first level and a second level during the on time of the switch. The control signal is responsive to the variable current limit threshold to regulate a power supply with an output characteristic having an approximately constant output voltage below an output current threshold and an approximately constant output current below an output voltage threshold.