In this research, we present a new approach for still image data compression. The first step is to decompose an image into small blocks of the same size via full wavelet transform (FWT), where each block corresponds to a particular frequency band whereas each transform coefficient in these blocks corresponds to a local spatial region in the original image. The space-frequency energy compaction property of the FWT is demonstrated. That is, most energy is concentrated in either low frequency blocks or transform coefficients associated with spatial regions with strong variations such as edges or textures. Image compression can be achieved by effectively using this energy compaction property. The second step is bit allocation and quantization. The block consisting of the lowest frequency components is quantized with 6 bits with the Gaussian density assumption. For coefficients in the remaining blocks, we propose a bit assignment scheme based on the block and position energy of the FWT coefficients. They are then quantized with either the Laplacian or the Gaussian density depending on the number of quantization levels. The relationship between the proposed method and other popular image compression methods such as DCT, PWT (pyramidal wavelet transform), and SBC (subband coding) is also discussed.