A wireless power system may use a wireless power transmitting device to transmit wireless power to a wireless power receiving device. The wireless power transmitting device may transmit wireless power at a wireless power transmission frequency. Wireless power signals at the wireless power transmission frequency can create interference with a sensitive electrical component in the wireless power receiving device when the wireless power transmission frequency lies in a sensitive frequency band associated with the component. Measurement circuitry in the wireless power receiving device can measure the wireless power transmission frequency. In response to determining that the wireless power transmission frequency lies in a sensitive frequency band, the wireless power receiving device may send an in-band wireless power level adjustment request to the wireless power transmitting device. The request causes a frequency adjustment that moves the wireless power transmission frequency out of the sensitive band.