Methods and apparatus for predistorting signals in a polar modulation transmitter. An exemplary method includes predistorting an envelope component signal in an amplitude path of a polar modulation transmitter according to a set of AM/AM predistortion coefficients, and predistorting a phase component signal in a phase path of the polar modulation transmitter according to a set of AM/PM predistortion coefficients. The AM/AM and AM/PM predistortion coefficients are stored in a memory in the form of a look up table (LUT). The envelope component signal is scaled and/or offset, before predistortion is applied, by an amount dependent upon which average power level of a plurality of average power levels the power amplifier of the polar modulation transmitter is configured to operate. Scaling and/or offsetting the envelope component signal prior to applying predistortion affords the ability to share the AM/AM and AM/PM predistortion coefficients of the predistortion LUT over the plurality of average power levels.