Abstract The sublimation of water in the region of extremely low pressures and temperatures meets increasing interest for the exploration of icy cosmic bodies. At temperatures below 130 K, the shape of the sublimation curve of H2O is not known; neither experimental data nor theoretical treatments exist for this region. Based upon theoretical upper and lower bounds for the heat capacity of water vapor in this range, a narrow region in the pressure–temperature diagram is identified which must necessarily enclose the sublimation curve down to virtually any lower pressures and temperatures. Within this region, an approximate sublimation curve is computed from the 2006 Gibbs potential of ice Ih, using available heat capacity data points of water vapor between 10 and 130 K. The theoretical zero-point limiting law of the sublimation pressure is derived. Valid between 20 and 273.16 K, correlation equations for the sublimation enthalpy and the sublimation pressure are fitted to the computed data. All quantities are expressed in the 1990 temperature scale ITS-90. Under cosmic conditions, our results suggest that the sublimation of ice is unlikely below 50 K and impossible below 23 K.