The improved multiband structured subband adaptive filter (IMSAF) utilizes the input regressors at each subband to speed up the convergence rate of MSAF. When the number of input regressors is increased, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. The current study introduces two new IMSAF algorithms with low computational complexity feature. In the first algorithm, a subset of input regressors at each subband is optimally picked out during the adaptation. In the second approach, the number of selected input regressors is dynamically changed at each subband for every iteration. The introduced algorithms are called selective regressor IMSAF (SR-IMSAF) and dynamic selective regressor IMSAF (DSR-IMSAF). The SR-IMSAF and DSR-IMSAF are shown to be capable of outperforming the full-update IMSAF while the computational complexity is kept low. In the following, the general update equation to establishment of the family of IMSAF algorithms is presented. Accordingly, the mean-square performance analysis of the algorithms is studied in a unified way and the general theoretical expressions for transient, steady-state, and the stability bounds for IMSAF, SR-IMSAF, and DSR-IMSAF are derived. The good performance of the introduced algorithms and the validity of the derived theoretical relations are justified by presenting various experimental results.