In previous work we considered LPVQ, a compression algorithm based on Locally Optimal Partitioned Vector Quantization that can be used to compress hyperspectral images by applying partitioned VQ to the spectral signatures (e.g., to the 224 16-bit values of a NASA AVIRIS pixel) and then encoding error information with a threshold that can be varied from high quality lossy to near lossless to lossless (e.g., 50-to-1 lossy, 10-to-1 near lossless, or 3-to-1 lossless). An advantage of LPVQ is extremely fast decoding (table lookup followed by entropy decoding), but it is at the cost of more complex encoding. Here we present a new low complexity algorithm for hyperspectral image compression, called SLSQ, that employs linear prediction targeted at spectral correlation followed by entropy coding of the prediction error. We then consider how SLSQ can be combined with LPVQ in a scenario commonly arising in practice. In this scenario, a low-complexity lossless encoder on the remote acquisition platform compresses the data for transmission to a central computing facility, where it is processed and recoded using LPVQ, so that the compressed data can be distributed to the final users at various quality levels. The VQ indices of the LPVQ form a lossy compressed image of only about 2% of the original size; this small image can be employed to greatly reduce the time for browsing and classification.