Hyperspectral sounder data is a particular class of data that requires high accuracy for useful retrieval of atmospheric temperature and moisture profiles, surface characteristics, cloud properties, and trace gas information. Therefore compression of these data sets is better to be lossless or near lossless. The next-generation NOAA/NESDIS GOES-R hyperspectral sounder, now referred to as the HES (Hyperspectral Environmental Suite), will have hyperspectral resolution (over one thousand channels with spectral widths on the order of 0.5 wavenumber) and high spatial resolution (less than 10 km). Given the large volume of three-dimensional hyperspectral sounder data that will be generated by the HES instrument, the use of robust data compression techniques will be beneficial to data transfer and archive. In this paper, we study lossless data compression for the HES using 3D integer wavelet transforms via the lifting schemes. The wavelet coefficients are then processed with the 3D embedded zerotree wavelet (EZW) algorithm followed by context-based arithmetic coding. We extend the 3D EZW scheme to take on any size of 3D satellite data, each of whose dimensions need not be divisible by 2N, where N is the levels of the wavelet decomposition being performed. The compression ratios of various kinds of wavelet transforms are presented along with a comparison with the JPEG2000 codec.