A voltage source provides an output voltage to drive a plurality of light emitting diode (LED) strings. A LED driver adjusts the level of the output voltage so as to maintain the lowest tail voltage of the LED strings at or near a predetermined threshold voltage so as provide sufficient headroom voltages for current regulators for the LED strings. The LED driver operates in an operational mode and a calibration mode, which can be implemented in parallel with, or part of, the operational mode. During the calibration mode, the LED driver determines, for each LED string, a code value representative of the level of the output voltage necessary to maintain the tail voltage of the corresponding LED string at or near the predetermined threshold voltage. In the operational mode, the code values from the calibration mode are used to control the voltage source to provide an appropriate level for the output voltage.