This paper describes a subspace clustering strategy for the spectral compression of multispectral images. Unlike standard PCA, this approach finds clusters in different subspaces of different dimension. Consequently, instead of representing all spectra in a single low-dimensional subspace of a fixed dimension, spectral data are assigned to multiple subspaces having a range of dimensions from one to eight. For a given compression ratio, this tradeoff reduces the maximum reconstruction error dramatically. In the case of compressing multispectral images, this initial compression step is followed by lossless JPEG2000 compression in order to remove the spatial redundancy in the data as well.