Envelope power supply circuitry includes an envelope power converter circuitry and envelope tracking circuitry. The envelope power converter circuitry receives an envelope power converter control signal from the envelope tracking circuitry and a supply voltage and provides an envelope power supply signal for an amplifier based thereon. In a first mode of operation, the envelope power converter control signal is provided such that the envelope power supply signal causes the gain of the amplifier to remain substantially constant over a range of input power provided to the amplifier. In a second mode of operation, the envelope power converter control signal is provided such that the envelope power supply signal remains substantially constant for values within the range of input power below a predetermined threshold, and such that the envelope power supply signal causes the gain of the amplifier to remain substantially constant for other values.