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Listless set partitioning embedded block (LSK) and set partitioning embedded block (SPECK) are known for their low complexity and simple implementation. However, the drawback is that these block-based algorithms encode each insignificant subband by a zero. This generates many zeros at earlier passes because the number of significant coefficients at higher bitplanes is likely to be very few in a transformed image. An improved LSK (ILSK) algorithm that codes a single zero to several insignificant subbands is proposed. This reduces the length of the output bit string, encoding/decoding time and dynamic memory requirement at early passes. Furthermore, ILSK algorithm is coupled with discrete Tchebichef transform (DTT). This gives rise to a novel coder named as hierarchical listless DTT (HLDTT). The proposed HLDTT has desirable attributes like full embeddedness for progressive transmission, precise rate control for constant bit rate traffic and low complexity for low power applications. The performance of HLDTT is assessed using peak-signal-to-noise-ratio (PSNR) and structural-similarity-index-metric (SSIM). Extensive simulation conducted on various standard test images shows that HLDTT exhibits significant improvement in PSNR values from lower to medium bit rates. At the same time, HLDTT shows improvement in SSIM values on all bit rates.