An electronic device may be provided with wireless circuitry for transmitting and receiving wireless signals. Control circuitry may be used to adjust transmit power levels for the wireless signals and other settings for the wireless circuitry. The electronic device may be operated in conjunction with an external accessory. The accessory may be equipment that includes a dock connector, a case to enclose the electronic device, equipment that is coupled to the electronic device using a cable, or other external electronic equipment. An identifier may be stored in the accessory. The impact of the accessory on the wireless performance of the electronic device may be characterized and associated with the identifier. During operation of the electronic device, the electronic device may adjust transmit power levels and other settings based on the identifier of the accessory and based on sensor data, user input, and other information.