An electronic device may include a display having an array of pixels and a backlight that provides backlight illumination for the array of pixels. The backlight may be a direct-lit backlight with a two-dimensional array of light-emitting diodes operable in a local dimming scheme. The electronic device may include control circuitry that provides pixel signals to the array of pixels and backlight signals to the backlight. The control circuitry may adjust the pixel signals and the backlight signals to compensate for brightness and color non-uniformity in the backlight. To compensate for image-dependent backlight non-uniformity, the control circuitry may simulate artificial backlight data based on the target image to be displayed and stored point spread information. To compensate for white-point-dependent backlight non-uniformity, the control circuitry may use measured actual backlight data that describes color variations across the backlight for a given target white point.