Capabilities and limitations of two fast radiative transfer models simulating cloudy spectra of the Infrared Atmospheric Sounding Interferometer (IASI) have been investigated in this paper. These models include a better modeling of the clouds than current operational fast forward models, such as scattering effects of the radiation in the cloud layer. An accurate simulation of the IASI spectra in the presence of ice clouds or for vertically extended clouds is a necessary step toward the use of these cloud-affected radiances in an operational context. Through a collocation of IASI observations with an independent data set from the Lindenberg ground-based station and the A-Train space-borne active instruments, this study first examines the accuracy of the fast radiative transfer models to simulate the cloudy spectra and provides some indications of confidence in the use of the cloud microphysical and optical properties. This first step shows the high sensitivity toward the cloudy inputs (crystal shapes, particle size, and cloud water content) which can reach several kelvins. It also provides a screening method to process cloudy radiances and to deal with the strong sensitivity of the fast radiative transfer model. The performance of the scattering fast radiative transfer models is then assessed in a global operational through simulations during a one week period over the globe, with the profiles of cloud variables from the ECMWF forecast used to compute the radiances. The applied screening method has reduced the standard deviation between simulated and observed spectra from 9 to 3 K.