In this paper, a new compression technique aiming at reducing the size of storage of multispectral images and maintaining at the same time the high-quality reconstruction is presented. An optimal multispectral band ordering process is applied before compression, and then, the dual-tree discrete wavelet transform is used in the spectral dimension, and the 2D discrete wavelet transform is used in the spatial dimensions. Finally, a simple Huffman coder is used for compression. Landsat ETM+ images are used for experimentations. Experimental results demonstrate that the proposed technique has better performance than JPEG, JPEG2000, SPIHT, and JPEG2000 with a 3D dual-tree transformation.