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A new approach of backward coding of wavelet trees (BCWT) is presented. Contrary to the common "forward" coding of wavelet trees from the highest level (lowest resolution), the new approach starts coding from the lowest level and goes backward by building a map of maximum quantization levels of descendants. BCWT eliminates several major bottlenecks of existing wavelet-tree-based codecs, namely tree-scanning, bitplane coding and dynamic lists management. Compared to SPIHT, BCWT encodes and decodes up to eight times faster without sacrificing PSNR. At the same time, BCWT provides desirable features such as low complexity, low memory usage, and resolution scalability.