An electronic device may be provided with a display mounted in a housing. The display may have an array of display pixels that provide light to a user. The array of display pixels may form active display structures with a rectangular shape. The rectangular active display structures may be surrounded by an inactive border region. Reflector structures may be used to reflect light that is emitted from peripheral portions of the active display structures to a portion of the display overlapping the inactive border region, thereby providing the display with an effective active area that is larger than the area of the active display structures. The reflector structures may include rotatable reflectors. Control circuitry may use a rotatable positioner to rotate rotatable reflector structures in synchronization with controlling which pixel data is displayed by the display pixels in the peripheral portions of the active display structures.