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A degree-k zero tree model is presented, in order to quantify the coding power of zerotrees in wavelet-based image coding. Based on the model, the coding behaviors of modern zerotree based image coders are clearly explained. Also, we explain why the well-known SPIHT algorithm can code a wider range of zerotrees than EZW. Experimental results support our idea that higher degree zerotree coder will have more coding power.