We have composed compression methods, which are based on the one-, two- and three-dimensional wavelet transforms. In addition, clustering the spectra of the image is considered. These compression methods, combining compression in the spectral and spatial domains, are compared by using a dataset of 65 multispectral images. The experimental results show that, at low compression ratios, the best method is based on the three-dimensional wavelet transform, where the spatial and spectral dimensions are transformed simultaneously. At higher compression ratios, a high quality wavelet-based compression method in the spatial dimensions combined with the principal component analysis in the spectral dimension gives the best results. This means that components of compressed images can be used as features in pattern analysis applications. The selection of the compression parameters is image-dependent. The results also show that, for multispectral images, both spectral and spatial compression could be used, and for best results, optimal bit allocation in encoding should be found. The results from the methods suggested are compared to the results found in the literature.