n this paper we focus on the compression of three-dimensional hyperspectral data, and review the state-of-the-art low-complexity Spectral-oriented Least SQuares (SLSQ) algorithm, which is suitable for on board implementations on airplanes or satellites. Two approaches for improving the compres- sion performances of SLSQ are considered: band ordering and band clustering. We experimentally test the performances of SLSQ on a test data set of five NASA AVIRIS hyperspectral images and the results obtained confirm the efficiency of the algorithm