An electronic device may have an antenna for providing coverage in wireless communications bands of interest such as a low frequency communications band and a high frequency communications band. The antenna may have an antenna ground and an antenna resonating element. The antenna resonating element may have a high band arm that contributes to a first high band resonance in the high band and may have a low band arm that exhibits a low band resonance in the low band. A passive filter that is coupled between first and second portions of the antenna resonating element may be configured to exhibit a short circuit impedance associated with a bypass path that allows the antenna resonating element to contribute to a second high band resonance in the high band. A tunable inductor coupled to the antenna resonating element may be used to tune the low band resonance.