Wavelet transform has recently been attracting notable attention in its applicability for a variety of signal processing or image coding1'2'3, since it is expected that wavelet provides a unified interpretation to transform coding, hierarchical coding, and subband coding, all of which have ever been studied separately. It is also expected that wavelet transform is shown to be more advantageous than other image coding schemes because the wavelet coefficients represent the features of an image localized both in spatial and frequency domains4'5. In case of transform coding or subband coding, the efficiency is generally maximized by designing bit allocation to each decomposed band signal proportional to the relative importance of information in it. This technique is known as the optimum bit allocation algorithm (OBA). However, OBA should not directly be applied to the wavelet coding, because OBA does not well exploit the spatial local information represented on each wavelet coefficient. The purpose of this work is to develop a quantization scheme which maintains significant spatial information locally represented on wavelet coefficients. Preserving only the selected coefficients which represent visually significant features and discarding the others, is expected to keep high image quality since the significant features will be kept even at a low bit rate. In this respect, we propose two kinds of image data compression techniques employing a selective preservation of wavelet coefficients. Section 2 gives a brief description of wavelet transform, which includes construction of wavelet basis functions, feature extraction with wavelet, and multi-resolution property of wavelet. In Section 3, the first technique is proposed where resolution dependent thresholding is introduced to classify wavelet coefficients into significant or insignificant ones. In Section 4, the second technique is proposed where better performance can be achieved by further classifying significant coefficients with a multiresolution property of wavelet. Finally, summary and conclusions are provided in Section 5.