Improvements in weather and climate observation, analysis, and prediction will be achieved through advances of contemporary and future ultraspectral infrared sounders such as Atmospheric Infrared Sounder (AIRS), Tropospheric Emission Spectrometer (TES), Geosynchronous Imaging Fourier Transform Spectrometer (GIFTS), and Hyperspectral Environmental Suite (HES). Given their unprecedented 3D data sizes to be generated each day, the use of robust data compression techniques will be beneficial to data transfer and archive. Lossless or near-lossless compression of this ultraspectral sounder data is desired to avoid potentially significant degradation of the geophysical parameter retrieval in an associated ill-posed inverse problem. In this paper we investigate various 2D and 3D compression techniques applicable to ultraspectral sounder data. These techniques include transform-based (JPEG2000, 3D-SPIHT), prediction-based (JPEG-LS, CALIC), and clustering-based (PVQ, DPVQ, PPVQ) compression methods. Data preprocessing schemes for compression gains are also illustrated.