The advance 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) will provide better weather prediction and climate monitoring. Lossless or near-lossless compression of ultraspectral sounder data is desired to avoid potentially significant degradation of the geophysical retrieval in the associated ill-posed inverse problem. Given the unprecedented 3D data size to be generated by a ultraspectral sounder each day, the use of robust data compression techniques will be beneficial to data transfer and archive. In this paper we demonstrate various 2D and 3D compression techniques applicable to ultraspectral sounder data. These techniques include projection-based, transform-based, prediction-based, clustering-based algorithms, and their combinations. Data preprocessing schemes for compression gains are also elaborated.