In the context of satellite image compression, we are interested in simultaneously exploiting the spatial and spectral activity of multispectral data by using improved lifting structures. The novelty of our approach lies in two aspects. Firstly, we employ nonseparable vector lifting structures that extend the conventional separable lifting scheme. Secondly, the problem of coding the resulting coefficients is addressed. More precisely, we propose an extension to the vector and nonseparable case of Shapiro's embedded zerotrees of wavelet coefficients which achieves further saving in the bitrate. Experimental results carried out on natural remote sensing images show the good performance of the proposed compression procedure.