An entropy efficient video coder for wavelet pyramids approaches the entropy-limited coding rate of video wavelet pyramids, is fast in both hardware and software implementations, and has low complexity (no multiplies) for use in ASICs. It uses a modified Z-coder to code the zero/non-zero significance function and Huffman coding for the non-zero coefficients themselves. The encoding unit includes a significance function generator that receives coefficients and outputs a single significance bit. A zero coefficient eliminator receives coefficients in parallel with the significance function generator and outputs coefficients if non-zero. Output from the significance function generator is coded using the modified Z-coder. Output from the zero coefficient eliminator is coded using Huffman coding. Both outputs are combined to form the resulting compressed stream. The modified Z-coder is similar to a standard Z-coder but uses a different technique for the LPS (least probable symbol) case during encoding and decoding that results in a Z-coder that functions appropriately.