An electronic device may be provided with wireless circuitry and control circuitry. The wireless circuitry may include an antenna with an inverted-F antenna resonating element formed from portions of a peripheral conductive electronic device housing structure and may have an antenna ground that is separated from the antenna resonating element by a gap. The antenna may include a first adjustable component coupled between the antenna resonating element arm and the antenna ground on a first side of the antenna feed and a second adjustable component coupled between the antenna resonating element arm and the antenna ground on a second side of the antenna feed. Control circuitry in the electronic device may adjust the first and second adjustable components between a first tuning mode, a second tuning mode, and a third tuning mode.