An electronic device may have a hybrid antenna that includes a slot resonating element formed from a slot in a ground plane and a planar resonating element formed over the slot. A parasitic element may be disposed over the planar element. A switch may couple the parasitic element to the ground. A tunable circuit may couple the planar element to the ground. The switch and tunable circuit may be placed in different tuning states. In a first state, the tunable circuit and switch form open circuits. In a second state, the tunable circuit may an open circuit and the switch is closed. In a third state, the tunable circuit forms a return path and the switch forms an open circuit. This may allow the antenna to operate with satisfactory efficiency in low, mid, and high bands despite volume constraints imposed on the antenna.