An electronic device may be provided with display circuitry that includes a display timing controller, a backlight driver, a light source, and other associated backlight structures. The backlight control circuitry may generate a control signal having an adjustable duty cycle to the backlight driver. The backlight driver may include a boost converter, a current driver, and backlight control circuitry. The current driver may only be activated when the control signal is high. The backlight control circuitry may output an enable signal to the boost converter. The backlight control circuitry may activate the boost converter a predetermined amount of time before each rising clock edge in the control signal by asserting the enable signal for a longer period of time than when the control signal is high. The control signal and the enable signal may be deasserted at around the same times.