An apparatus and a method select and use parameter values for an RF power amplifier linearizer to pre-distort the input signals of a power amplifier, so as to achieve a linear output response in the power amplifier. The apparatus and the method select from a number sets of parameter values, each set of parameter values corresponding to a different output power range of the power amplifier. The set of parameters include a coefficient vector tailored for the particular output power range for that set. The power amplifier input power is repeatedly measured and filtered at various time intervals. The input power measurements may be filtered by a fast attack/slow decay filter, which follows the peaks of the measurements under operation of the fast attack portion of the filter and provides a low variance during operation of the slow decay portion of the filter. The coefficient values for the predistortion linearization of the power amplifier is adapted dynamically, in response to changes in the input power level of the power amplifier. In one embodiment, hysteresis is used to reduce the rate at which the predistortion linearizer hops between two sets of the parameter values. Using the apparatus and the method, good ACLR across a wide range of power amplifier output power is achieved. Such characteristics are particularly advantageous in a system in which waveforms having fast power transients are present.