A handheld electronic device is provided that contains wireless communications circuitry. The wireless communications circuitry may include antennas. An antenna in the handheld electronic device may have a ground plane element. A slot antenna resonating element may be formed from an opening in the ground plane element. A near-field-coupled antenna resonating element may be electromagnetically coupled to the slot antenna resonating element through electromagnetic near-field coupling. A transmission line may directly feed the slot antenna resonating element. The transmission line may indirectly feed the near-field-coupled antenna resonating element through the slot antenna resonating element. The slot antenna resonating element may have one or more associated resonant frequencies and the near-field-coupled antenna resonating element may have one or more associated resonant frequencies. The antenna may be configured to cover one or more distinct communications bands.