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This paper addresses the problem of prioritizing, i.e., preserve with higher fidelity, region-of-interest during image compression. Regions-of-interest are found, for example, in medical imagery where only a small area is useful for diagnostic, or in surveillance images where targets have to be identified and tracked. These ROI are often characterized by their fine details which therefore need to be preserved if the image is to be of any use after it is decompressed. Wavelet-based image compression is appropriate for such tasks because of its localization property. The authors present an algorithm, based on Shapiro's popular EZW (embedded image coding using zerotree of wavelet coefficients) to prioritize region-of-interest. A nonuniform quantizer with smaller steps for smaller coefficients is used on the coefficients of the ROI. This allows to transmit initially the fine details of the ROI and to use successive approximation quantization to reduce the quantization error on larger coefficients of the image, ROI or non-ROI. Simulation results show that this approach allows to efficiently preserve the fine details of the ROI.