An RF transmitter (30) includes an RF power amplifier (32) for which the power input bias voltage (40) and signal input bias voltage (80) are controlled within feedback loops. A peak detector (44) generates a lowered-spectrum, peak-tracking signal (34) that follows the largest amplitude peaks of a wide bandwidth communication signal (16) but exhibits a lower bandwidth. This signal (34) is scaled in response to the operation of a drain bias tracking loop (146) then used to control a switching power supply (36) that generates the power input bias voltage. The tracking loop (146) is responsive to out-of-band power detected in a portion of the amplified RF communication signal (16″). A ratio of out-of-band power (128) to in-band power (126) is manipulated in the tracking loop (146) so that the power input bias voltage is modulated in a way that holds the out-of-band power at a desired predetermined level.