A display may be provided with integral touch functionality. The display may include a common electrode layer having row electrodes arranged in rows and column electrodes interposed between the row electrodes of each row. The row electrodes may be electrically coupled by conductive paths. The row and column electrodes may be coupled to touch sensor circuitry that uses the row and column electrodes to detect touch events. Each electrode of the common electrode layer may cover a respective portion of an array of pixels. Each pixel of the display may have a respective aperture. The conductive paths that electrically couple row electrodes of the common electrode layer may cover or otherwise block some light from passing through pixels, resulting in reduced apertures. Dummy structures may be provided for other pixels that modify the apertures of the other pixels to match the reduced apertures associated with the conductive paths.