This study examines the information content on atmospheric temperature and humidity profiles that could be provided by a future spaceborne microwave sensor with a few hundred radiances in the millimetre and submillimetre spectral domains (ranging from 7–800 GHz). A channel selection method based on optimal estimation theory is undertaken, using a database of profiles with associated errors from the European Centre for Medium-Range Weather Forecasts (ECMWF) numerical weather prediction model and the radiative transfer model Atmospheric Radiative Transfer Simulator (ARTS) under clear-sky conditions. The main results indicate that, by increasing the number of channels within the oxygen absorption band around 60 GHz and within the water-vapour absorption band at 183 GHz, the accuracy of temperature and humidity retrievals in the troposphere and stratosphere (for temperature) would be noticeably improved compared with present and planned microwave radiometers. The channels located in the absorption lines at 118 GHz and above 200 GHz do not bring significant additional information regarding atmospheric profiles under clear-sky conditions, partly due to greater radiometric noise. With a set of 137 selected channels that contribute to 90% of the total information content (measured by the degree of freedom for signal), it is possible to achieve almost the same performance in terms of variance error reduction as with 276 candidate channels. Sensitivity studies of various prescribed quantities defining the channel selection have been undertaken, in order to check the robustness of the conclusions. They show that none of the choices modifies the above findings.