A display may be based on a display unit that is mounted within a chassis. The display unit may be a liquid crystal display unit. A backlight may be used to illuminate the display unit. The backlight may include a light guide plate. Light from a light source may be launched into an edge of the light guide plate. Scattered light from the light guide plate may travel vertically along a vertical axis that is perpendicular to the plane that contains the light guide plate. The scattered light may pass through the display unit and may serve as backlight for the display. The light guide plate may be mounted within a rectangular opening in the chassis. The edges of the rectangular opening and the edges of the light guide plate may be configured to reduce excessive reflections. These edges may have reflection-reducing coatings, non-planar surfaces, and other reflection-reducing configurations.