Electronic device with proximity-based radio power control

A method of controlling radio-frequency cellular telephone signal transmit power through an antenna in a handheld electronic device that is used by a user having a head, wherein the handheld electronic device includes circuitry that handles radio-frequency wireless transmissions in at least a first wireless communications band and a second wireless communications band, the method comprising:

• with a sensor in the handheld electronic device, determining whether the head of the user is present within a given distance of the handheld electronic device,
• when it is determined from the sensor that the head of the user is not present within the given distance of the handheld electronic device, establishing a first maximum allowable level for the transmit power with the circuitry;
• when it is determined from the sensor that the head of the user is present within the given distance of the handheld electronic device, establishing a second maximum allowable level for the transmit power with the circuitry, wherein the second maximum allowable level for the transmit power is less than the first maximum allowable level for the transmit power;
• and
• with the circuitry, making radio-frequency wireless transmit power adjustments in the first wireless communications band that reduce the transmitted power by the handheld electronic device in the first wireless communications band at least partly in response to an increase in radio-frequency wireless transmit power levels by the handheld electronic device in the second wireless communications band.