Electronic devices may include radio-frequency transceiver circuitry and antenna structures. The antenna structures may include antenna resonating elements such as dual-band antenna resonating elements that resonate in first and second communications bands. The antenna structures may also contain parasitic antenna elements such as elements that are operative in only the first or second communications band and elements that are operative in both the first and second communications bands. The antenna resonating elements and parasitic elements may be mounted on a common dielectric carrier. The dielectric carrier may be mounted within a slot or other opening in a conductive element. The conductive element may be formed from conductive housing structures in an electronic device such as a portable computer. The portable computer may have a clutch barrel with a dielectric cover. The dielectric cover may overlap and cover the slot and the dielectric carrier.