A wireless power receiving device has a coil that receives wireless power signals from a wireless power transmitting device and has a rectifier that produces direct-current power across rectifier output terminals using the received wireless power signals. A load in the wireless power receiving device receives a direct-current output voltage from the rectifier output terminals. In-band communications are supported in which an amplitude-shift keying communications scheme or other communications scheme is used by a data transmitter in the wireless power receiving device to transmit in-band data through the coil. In-band data is transmitted by modulating one or more transistors that are coupled to the coil and other wireless power receiving circuitry in series with one or more capacitors and is transmitted by modulating current flow through a ballast transistor or other adjustable load that is coupled across the rectifier output terminals.