The nonlinearities of power amplifiers combined with non-contiguous transmissions found in modern, frequency-agile, wireless standards create undesirable spurious emissions through the nearby spectrum of data carriers. Digital predistortion (DPD) is an effective way of combating spurious emission violations without the need for a significant power reduction in the transmitter leading to better power efficiency and network coverage. In this paper, an iterative, multi sub-band version of the sub-band DPD, proposed earlier by the authors, is presented. The DPD learning is iterated over intermodulation distortion (IMD) sub-bands until a satisfactory performance is achieved for each of them. A sequential DPD learning procedure is also presented to reduce the hardware complexity when higher order nonlinearities are incorporated in the DPD learning. Improvements in the convergence speed of the adaptive DPD learning are also achieved via incorporating a variable learning rate and interpolation of previously trained DPD coefficients. A WarpLab implementation of the proposed DPD is also shown with excellent suppression of the targeted spurious emissions.