A wireless electronic device may contain multiple antennas. Control circuitry in the wireless electronic device may adjust antenna switching circuitry so that the device repeatedly cycles through use of each of the antennas. In a device with first and second antennas, the device may repeatedly toggle between the first and second antennas. During each toggling cycle time period, the first antenna may transmit for a fraction of the time period and the second antenna may transmit for a fraction of the time period. The wireless device may control the average power emitted by each antenna by adjusting the fractions of time assigned to each antenna. By performing antenna toggling, the average transmit power produced by each antenna may be reduced while maintaining the average transmit power produced by the device at a desired level.