Disclosed are implementations, including a method for digital predistortion of multiband signals that includes receiving an input signal comprising multiple signal portions in different frequency bands, the input signal configured to be processed by a transmit chain, of a power amplification system, comprising at least a power amplifier that produces output with non-linear distortions, with the non-linear distortions of the transmit chain being represented using a set of basis functions derived according to a single-band model of the non-linear distortions. The method further includes performing digital predistortion on signal components derived from the multiple signal portions of the input signal using a reduced set of the basis functions that excludes at least some basis functions for at least some cross-terms resulting from a full expansion of the single-band model applied to the multiple signal portions, to produce a digital predistorted signal provided to the transmit chain.