Electronic devices are provided that contain wireless communications circuitry. The wireless communications circuitry may include radio-frequency transceiver circuitry and antenna structures. A display may be mounted on a front face of an electronic device. A conductive member such as a bezel may surround the display. Internal housing support structures such as a metal midplate member may be used to support the display. The midplate member may be connected between opposing edges of the bezel. The antenna structures may include an antenna formed from part of the midplate member and part of the bezel. Antenna image currents in the midplate member may be blocked by slots in the midplate member. The slots may be located adjacent to the antenna and may ensure that the antenna emits radio-frequency signals in a desired pattern. The slots may be angled and segmented.