Remote sensing produces large amounts of digital data that is collected into databases. Since a variety of applications utilize multispectral data, the data cannot be compressed with lossy methods for some user communities. In this paper, we propose improvements for the combination of two reversible methods for the lossless compression of multispectral images. Our improvements are three-fold: number of bits allocated to the coefficients from PCA is not constant but it is based on heuristics, difference between consecutive coefficients are entropy-coded, also the back-end is modified so that all bands are separately entropy coded, i.e. instead of one entropy coder, we used several. Depending on the AVIRIS image, the actual compression ratios, calculated from the files sizes, were in the range from 3.05 to 3.21.