A novel digital baseband predistorter with improved reduction of spectral regrowth is proposed and investigated. The improvements are achieved by using a proposed predistortion technique and extended power amplifier fundamental-frequency modelling. The digital baseband predistortion (DPD), known for its simplicity of realisation, low cost and integrability, however, suffers from poor linearizing performances. We incorporate baseband iterative injection of in-band distortion components into the baseband DPD in order to enhance the nonlinearity compensation. General formulas for the fundamental-frequency output of a power amplifier (PA) with n-order nonlinearity and recursive formulas for calculating the injected components for different number of iterations are developed. The proposed iterative digital baseband predistorter is verified experimentally with a wireless power amplifier and measured results are presented to demonstrate feasibility of the proposed concept. The spectral regrowth suppression of 20 dB is achieved for a 3.5 MHz digitally modulated signal.