An electronic device may be provided with a display. The display may include a backlight having an array of locally dimmable light sources. Control circuitry may provide control signals to the backlight to produce light at different brightness levels. When the brightness level is below a threshold, the control circuitry may use pulse-width-modulation control signals to control the light sources in the backlight. When the brightness level is above the brightness threshold, the control circuitry may use analog control signals to control the light sources in the backlight. The control circuitry may adjust the threshold to achieve different dimming ranges for different brightness settings. A low brightness setting, for example, may have a lower threshold and lower dimming range than a high brightness setting, which may help produce darker darks when the display operates in a low brightness setting.