Electronic devices may include displays. A display may include backlight structures that generate light and display layers that generate images using the generated light. An electronic device may include an opaque flexible printed circuit that is wrapped around one or more edges of the backlight structures. The opaque flexible printed circuit may prevent light from the backlight structures from reaching other electronic components or escaping from the device. The opaque flexible printed circuit may include signal lines that communicate signals between a printed circuit board and the display. The opaque flexible printed circuit may be a layer of the printed circuit board that extends from an edge of the printed circuit board. The printed circuit board may include an additional flexible extended printed circuit layer that wraps around a surface of the printed circuit board and forms a portion of a conductive shield over that surface.