This paper examines the problem of compressing multispectral images using the wavelet transform and stack-run entropy coding. Our goal is to explore various ways of coding the wavelet coefficients in order to see which techniques can best exploit the correlation between the multispectral bands to produce an efficient coding algorithm. The results of our study indicate that applying the KLT to each subband followed by lattice VQ on Zn and subsequent independent entropy coding of each of the lattice dimensions is an effective and fairly simple coding technique. We also demonstrate the importance of proper bit-allocation or, equivalently, the correct choice of the lattice scale parameter for each subband