The zero-memory set partitioned embedded block (ZM-SPECK) algorithm is a memory efficient block-based image coder used to encode the wavelet transformed images. It is a listless form of the SPECK algorithm and has no provision for saving the significance information for various coefficients/sets. Since it performs significance testing of sets recursively at each bit-plane, therefore it is computationally complex. Due to this limitation, it is difficult to implement it on low resource sensor/IoT nodes. In this paper, its low complexity version named Modified Zero Memory Set Partitioned Embedded Block (MZM-SPECK) is proposed which reduces the recursive significance test of sets. The simulation results indicate that the proposed algorithm surpasses other wavelet-based coders with regard to memory and computational complexity while maintaining the excellent coding efficiency.