A radio-frequency (RF) transmitter power amplifier circuit provides for practically linear performance by predistorting the amplifier input signals to compensate for amplifier distortion at high power levels, and provides a fine degree of control of amplifier power needed to handle complex modulation schemes with widely and rapidly varying power requirements. A predistortion database (20) contains gain and phase corrections for various transmission types and a separate automatic gain control database (38) contains fine amplifier gain corrections. A real-time processor (26) combines the two types of corrections and applies them to the amplifier input signals, and a background processor (16) continually updates both databases in accordance with a programmable priority scheme. Integration of predistortion and amplifier power control is achieved in a manner that minimizes adverse effects of one type of control on the other. One feature of the invention provides for rapid convergence of the predistortion correction.