The Infrared Atmospheric Sounding Interferometer (IASI) system provides infrared soundings of moisture and temperature profiles, as well as soundings of chemical components. These measurements play a key role in atmospheric chemistry, global change, and climate monitoring. The instrument, developed by a cooperating agreement between European Organisation for the Exploitation of Meteorological Satellites and Centre National d'Études Spatiales, is implemented on the Metop satellite series. The instrument data production rate is 45 Mb/s while the transmission rate allocated to IASI measurements is 1.5 Mb/s. It is thus necessary to implement a significant part of the IASI data processing on-board the instrument. We investigate the information statistics of IASI L0 data once the on-board processing chain is finished. We analyze order-0 entropy, and order-1, order-2 and order-3 conditional entropies, where conditional entropies assess both the spectral and the spatial joint information. According to the simple order-0 entropy, at least one bit per sample could be spared if a variable-length code was employed. We also investigate the actual performance of different lossless compression techniques on IASI L0 data. The CCSDS-123, JPEG-LS, and JPEG2000 standards, as well as M-CALIC coding technique are evaluated. Experimental results reveal that IASI Level 0 data can be coded by a compression ratio above 2.6:1.