The technique of partially scanned interferograms is applied to the retrieval of trace gases from Infrared Atmospheric Sounding Interferometer (IASI) observations. For the specific case of CO, CO₂, CH₄ and N₂O, we show that this methodology allows us to retrieve trace gases column abundances at an unprecedented accuracy at the level of the single IASI footprint. The technique consists in transforming the IASI spectra back to the interferogram domain where we identify small regions that are mostly sensitive to single gas species. The retrieval is then performed by directly applying Least Squares estimation to these small segments of interferometric radiances. One of the main advantages of the technique is that it allows the efficient use of the information contained in all the IASI channels that are available in the absorption bands of a specific gas species. The retrieval technique has been applied to IASI radiances measured over the Mediterranean sea during the month of July 2010, one of the hottest months on record. Results have been validated against ground-based measurements. We have also carried out a comparison with Atmospheric Infrared Radiometer Sounder data and IASI retrievals obtained with usual variational approaches in the spectral domain.