Hyperspectral image data presents challenges to current transmission bandwidth and storage capabilities. To overcome these challenges and to retain the radiometric accuracy of the data, there is a need for good hyperspectral lossless compression. The current state-of-the-art lossless compression algorithm is JPEG-LS, which uses a 2-D edge-detecting predictor. Hyperspectral systems sample the electromagnetic spectrum very finely, which results in increased spectral correlation. A predictor that takes into account previous band information can obtain substantial gains in compression ratio. This paper discusses a number of different predictors that take advantage of the significant band-to-band (spectral) correlation within the hyperspectral imagery. A sample set of HYDICE, AVIRIS, and SEBASS imagery was used to evaluate the different predictors. While the JPEG-LS algorithm achieved just greater than 2:1 on most imagery, some of the 3-D prediction techniques achieved greater than 3:1 compression ratio. The characteristics of these test images and results from different predictors are presented in this paper.