A process for producing polyurethane foams, in which compositions comprising A) isocyanate-functional prepolymers obtainable by the reaction of A1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol with A2) polyalkylene oxides having an OH functionality of two or more, A3) optionally further isocyanate-reactive components not covered by A2); B) water in an amount of at least 2% by weight, based on the total weight of the composition; C) optionally heterocyclic 4-membered or 6-membered ring oligomers of low molecular weight diisocyanates having a molar mass of 140 to 278 g/mol, D) optionally catalysts; E) optionally salts of weak acids, the corresponding free acids of which have a pKA in water at 25°C of ≥ 3.0 and ≤ 14.0; F) optionally surfactants; and G) optionally mono- or polyhydric alcohols or polyols; H) optionally hydrophilic polyisocyanates obtainable by reaction of H1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol and/or polyisocyanates preparable therefrom and having an isocyanate functionality of 2 to 6 with H2) monofunctional polyalkylene oxides of OH number from 10 to 250 and of ethylene oxide content from 50 to 100 mol%, based on the total amount of the oxyalkylene groups present, are provided, foamed and cured, wherein the isocyanate-containing components, especially components A, C and H, have a total isocyanate content, determined by volumetric means according to DIN-EN ISO 11909, within a range from 2% to 8% by weight and a content of urethane groups, determined by the method specified in the description, of 1.0 to 3.5 mol/kg, based in each case on the total amount of the isocyanate-containing components. A) isocyanate-functional prepolymers obtainable by the reaction of A1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol with A2) polyalkylene oxides having an OH functionality of two or more, A3) optionally further isocyanate-reactive components not covered by A2); A1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol with A2) polyalkylene oxides having an OH functionality of two or more, A3) optionally further isocyanate-reactive components not covered by A2); B) water in an amount of at least 2% by weight, based on the total weight of the composition; C) optionally heterocyclic 4-membered or 6-membered ring oligomers of low molecular weight diisocyanates having a molar mass of 140 to 278 g/mol, D) optionally catalysts; E) optionally salts of weak acids, the corresponding free acids of which have a pKA in water at 25°C of ≥ 3.0 and ≤ 14.0; F) optionally surfactants; and G) optionally mono- or polyhydric alcohols or polyols; H) optionally hydrophilic polyisocyanates obtainable by reaction of H1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol and/or polyisocyanates preparable therefrom and having an isocyanate functionality of 2 to 6 with H2) monofunctional polyalkylene oxides of OH number from 10 to 250 and of ethylene oxide content from 50 to 100 mol%, based on the total amount of the oxyalkylene groups present, are provided, foamed and cured, H1) low molecular weight diisocyanates of molar mass from 140 to 278 g/mol and/or polyisocyanates preparable therefrom and having an isocyanate functionality of 2 to 6 with H2) monofunctional polyalkylene oxides of OH number from 10 to 250 and of ethylene oxide content from 50 to 100 mol%, based on the total amount of the oxyalkylene groups present,