An electronic device may have a liquid crystal display with backlight structures. The backlight structures may produce backlight that passes through the display layers in the display. The display layers may include a layer of liquid crystal material interposed between a color filter layer and a thin-film transistor layer. The backlight structures may include a light guide plate. A plurality of light-emitting diodes mounted on a flexible printed circuit may be coupled to an edge of the light guide plate. The flexible printed circuit may be curled into a spring element to bias the light-emitting diodes against the edge of the light guide plate. A plurality of gaps may be formed in the flexible printed circuit and may be used to separate and mechanically decouple adjacent light-emitting diodes. Individual light-emitting diodes may independently register to the light guide plate to maximize optical efficiency in the display.