In a wireless power transfer operation, the operating parameters are adjusted to improve efficiency by reducing the transmit and receive coil currents as follows. First, the transmitter causes the receiver to reduce the receive coil current to the lowest value based on the transmitter/receiver communication while still delivering the same amount of power to the load as before the AC current was adjusted to the minimum value. Then the transmitter may change the operating parameters to increase or preserve the power provided to the receiver without decreasing efficiency or with only small decrease in efficiency, or with increasing the efficiency. For example, the transmitter may increase the VBRG voltage (the DC voltage powering the transmit coil) or the operating frequency to maintain or increase output power levels at lower or the same AC and DC current levels. Other features are also provided.