The problem of reducing the dimensionality of infrared atmospheric sounding interferometer (IASI) data space through a suitable transform and performing the retrieval process for thermodynamical parameters within the transformed data space is addressed in this paper. The reduction of dimensionality is performed with the principal components transform, which allows us to represent the full IASI spectrum with a few coefficients of the expansion. This truncated expansion could have a twofold beneficial effect: (i) it could improve the present exploitation and performance of IASI data for the retrieval of temperature and moisture; and (ii) it could save transmission bandwidth, data rate and costs for the dissemination to users of IASI data. A suitable form of the inverse/forward model completely embedded in the transformed space has been derived and applied to simulated and real IASI data. This methodology has allowed us to assess the IASI performance for temperature, water vapor and ozone based on the full IASI spectral coverage. The use of back‐transformed spectral radiances (i.e. the filtered radiances obtained by the truncated expansion) instead of expansion coefficients has also been addressed and assessed. Retrieval exercises performed in simulation and with real observations lead us to conclude that the principal components space‐based inverse approach is potentially superior over the current practice of using sparse channels. Copyright © 2011 Royal Meteorological Society