Electronic devices may be provided that contain wireless communications circuitry. The wireless communications circuitry may include radio-frequency transceiver circuitry and antenna structures. The antenna structures may form a dual arm inverted-F antenna. The antenna may have a resonating element formed from portions of a peripheral conductive electronic device housing member and may have an antenna ground that is separated from the antenna resonating element by a gap. A short circuit path may bridge the gap. An antenna feed may be coupled across the gap in parallel with the short circuit path. Low band tuning may be provided using an adjustable inductor that bridges the gap. The antenna may have a slot-based parasitic antenna resonating element with a slot formed between portions of the peripheral conductive electronic device housing member and the antenna ground. An adjustable capacitor may bridge the slot to provide high band tuning.