An electronic device antenna may be provided with an antenna ground. An antenna resonating element may have a first end that is coupled to the ground using an inductor and may have a second end that is coupled to a peripheral conductive housing member in an electronic device. The peripheral conductive housing member may have a portion that is connected to the ground and may have a portion that is separated from the ground by a gap. The gap may be bridged by an inductor that couples the second end of the antenna resonating element to the antenna ground. The inductor may be bridged by a switch. A tunable circuit such as a capacitor bridged by a switch may be interposed in the antenna resonating element. The switches that bridge the gap and the capacitor may be used in tuning the antenna.