A display may have curved edges such as rounded corners. Pixels in the display may be controlled so that the active area of the display has the desired curved edge shape. In order to maximize the apparent smoothness of the curved edge, the display may include circuitry that dims some of the pixels based on their location relative to a spline for the curved edge. The display circuitry may include a multiplication circuit that receives image data as a first input and dimming factors from a gain table as a second input. The image data may include a brightness level for each pixel in the array of pixels. The multiplication circuit may multiply the brightness level for each pixel by its respective dimming factor. This modified image data may then be supplied to the imaging pixels using display driver circuitry.