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.