The Improved Multiband-structured Subband Adaptive Filter (IMSAF) applies the input regressors at each subband to speed up the convergence rate of Multiband- Structure Subband Adaptive Filter (MSAF). When the projection order increases, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. The present research introduces two new IMSAF algorithms with low computational complexity feature. In the first algorithm, the Selective Partial Update (SPU) approach is extended to IMSAF algorithms and SPU-IMSAF is established. In SPU-IMSAF, the filter coefficients are partially updated at each subband for every adaptation. In the second algorithm, the Set-Membership (SM) strategy is utilized in IMSAF and SM-IMSAF is established. The SM-IMSAF has a fast convergence rate, low steady-state error, and low computational complexity features at the same time. Also, by combining SM and SPU methods, the SM-SPU-IMSAF is introduced. Simulation results demonstrate the good performance of the proposed algorithms.