An electronic device may be provided with peripheral conductive housing structures, a first antenna, and a second antenna. A gap may divide the housing structures into a first segment forming an arm of the first antenna and a second segment forming an arm of the second antenna. A first feed terminal may be coupled to the first segment and a second feed terminal may be coupled to the second segment. Switchable components may be coupled in parallel between the first and second feed terminals across the gap. The switchable components may be adjusted to tune the frequency response of the first and/or second antenna. The switchable components may have a first state in which only the first feed terminal feeds the first antenna and may have a second state in which both the first and second feed terminals feed the first antenna.