In this paper the Integer Wavelet Transform (IWT) is described and compared with the classical real valued Discrete Wavelet Transform (DWT); it is shown that, with a simple and computationally inexpensive modification of the algorithm, the performance of the IWT can be raised to that of the DWT, so overcoming a limitation which is reported in the literature. Then, a new application of the Lifting Scheme to the generation of Integer Wavelet Packets (IWP) is presented. IWP yields a representation which can be loss-less, as it maps an integer valued sequence onto integer valued coefficients in the transformed domain; moreover, it allows for the selection of an adaptive representation, which can match the variable characteristics of SAR images better than the DWT. The proposed image compression scheme is based on the classical Coifman and Wickerhauser algorithm for best basis selection, applied to the IWP tree. Extensive simulations have proven that the proposed algorithm yields good performance for both generic and SAR images.