An electronic device may be provided with an organic light-emitting diode display with minimized border regions. The border regions may be minimized by providing the display with bent edge portions having neutral plane adjustment features that facilitate bending of the bent edge portions while minimizing damage to the bent edge portions. The neutral plane adjustment features may include a modified backfilm layer of the display in which portions of the backfilm layer are removed in a bend region. A display device may include a substrate, a display panel on the substrate having display pixels, and peripheral circuitry proximate the display panel and configured to drive the display pixels. A portion of the periphery of the substrate may be bent substantially orthogonal to the display panel to reduce an apparent surface area of the display device. The bent portion may include an electrode for communication with the peripheral circuitry.