Atmospheres are products of time-integrated mass exchange between the surface of a planet and its interior. On Earth and other planetary bodies, magma oceans likely marked significant atmosphere-forming events, during which both steam- and carbon-rich atmospheres may have been generated. However, the nature of atmospheres around rocky planets remains unclear for lack of constraints on their solubilities in liquids of appropriate composition. Here we determine the solubility of water in 14 peridotite liquids, representative of Earth’s mantle, synthesised in a laser-heated aerodynamic levitation furnace. We explore oxygen fugacities (fO2) between -1.9 and +6.0 log units relative to the iron-wüstite buffer at constant temperature (1900±50 °C) and pressure (1 bar). The resulting fH2O ranged from 0 to 0.027 bar and fH2 from 0 to 0.064 bar. Total H2O contents were determined by transmission FTIR spectroscopy of doubly-polished thick sections from the intensity of the absorption band at 3550 cm-1 and applying the Beer-Lambert law. The mole fraction of water in the liquid is found to be proportional to (fH2O)0.5, attesting to its dissolution as OH. The data are fitted by a solubility coefficient of ~525 ppm/bar0.5, roughly 25 % lower than for basaltic liquids at 1350 °C and 1 bar. Higher temperatures (rather than more magnesian compositions) result in a decrease of water solubility in silicate melts. Because the solubility of water remains high relative to that of CO2, steam atmospheres are rare, although they may form under moderately oxidising conditions on telluric bodies, given sufficiently high H/C ratios.