A transmitter generates first and second constant-envelope radio frequency (RF) component signals having first and second phase angles. The first and second phases are controlled by a phase controller. First and second nonlinear power amplifiers (PAs) are modulated by an amplitude-modulated power supply signal as the first and second constant-envelope RF component signals are amplified. The phase controller controls the first and second phases of the first and second constant-envelope RF component signals, in response to a power control signal, and, in so doing, controls an effective load impedance seen at the outputs of the first and second nonlinear PAs. By controlling the effective load impedance in response to a power control signal, rather than in response to rapid amplitude variations in an input signal envelope, the output power of the transmitter is efficiently controlled over a wide dynamic range even at low output powers.