An electronic device may have a liquid crystal display with backlight structures. The backlight structures may produce backlight that passes through display layers in the display. The display layers may include color filter elements, a liquid crystal layer, and a thin-film transistor layer. The backlight structures may have a light guide plate with opposing first and second edges. The light guide plate and other display layers may be assembled within support structures such as a metal chassis and a plastic chassis. A first strip of light-emitting diodes may be attached to the first edge of the light guide plate in a position that is floating with respect to the metal chassis. A second strip of light-emitting diodes may be attached to the second edge of the light guide plate in a position that is fixed with respect to the metal chassis.