An electronic device may have wireless circuitry with antennas. An antenna resonating element arm for a given antenna may be formed from metal structures supported by a plastic carrier. The antenna resonating element arm may be coupled to switching circuitry to isolate the antenna resonating element arm when the antenna resonating element arm is not being used to handle communications in a communications band. The electronic device may have a metal housing. A slot may separate a peripheral portion of the housing such as a sidewall portion from a planar rear portion. The sidewall portion and the planar rear portion may form an additional antenna that operates at communications frequencies outside of the communications band handled by the given antenna. A parasitic antenna resonating element arm may be formed in the slot to enhance the frequency response of the additional antenna.