Passive submillimeter-wave sensors are a way to obtain urgently needed global data on ice clouds, particularly on the so far poorly characterized 'essential climate variable' ice water path (IWP) and on ice particle size. CloudIce was a mission proposal to the European Space Agency ESA in response to the call for Earth Explorer 8 (EE8), which ran in 2009/2010. It proposed a passive submillimeter-wave sensor with channels ranging from 183 GHz to 664 GHz. The article describes the CloudIce mission proposal, with particular emphasis on describing the algorithms for the data-analysis of submillimeter-wave cloud ice data (retrieval algorithms) and demonstrating their maturity. It is shown that we have a robust understanding of the radiative properties of cloud ice in the millimeter/submillimeter spectral range, and that we have a proven toolbox of retrieval algorithms to work with these data. Although the mission was not selected for EE8, the concept will be useful as a reference for other future mission proposals.