Aspects of the subject technology relate to display circuitry such as backlight control circuitry for operating parallel strings of light-emitting diodes (LEDs). A voltage supply circuit of the backlight control circuitry provides a common supply voltage to the strings of LEDs. Headroom control circuitry samples a residual voltage at the end of each string, determines a minimum of the residual voltages, and provides feedback, based on the determined minimum voltage, to the voltage supply circuit. A headroom control feedback loop may be provided including sampling lines coupled to the second end of each string of LEDs for sampling a residual voltage of each string. Headroom control circuitry may modify the supply voltage based on the minimum residual voltage. Sample-and-hold circuitry may be provided that holds the sampled residual voltages until the voltage supply circuit is ready for an update.