An approach to digital compensation uses a particular structure for a digital pre-distorter (DPD) which acts as a relatively accurate pre-inverse of a non-linear circuit (e.g., a non-linear transmit chain involving digital-to-analog converter (DAC), lowpass filter, modulator, bandpass filter, and power amplifier) while making use of a relatively small number of parameters that characterize the non-linearity and/or parameters that provide accurate linearization without requiring continual updating.