A class of image compression algorithms has been developed for exploiting dependencies between the hierarchical wavelet coefficients using zerotrees. The paper deals with a fuzzy inference filter for image entropy coding by choosing significant coefficients and zerotree roots in the higher frequency wavelet subbands. Moreover, an adaptive quantization is proposed to improve the coding performance. Evaluating with the popular images, the proposed approach is comparable or superior to most state-of-the-art coders.