Process for preparing hydrophilic aliphatic polyurethane foams wherein compositions comprising A) hydrophilic polyisocyanates obtainable by reaction of A1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol and/or polyisocyanates obtainable therefrom with an isocyanate functionality of 2 to 6, with A2) monofunctional polyalkylene oxides having an OH number of 10 to 250, and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present, B) heterocyclic 4-ring or 6-ring oligomers of low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol, C) water, D) optionally catalysts, E) optionally C 8 to C 22 monocarboxylic acids or their ammonium or alkali metal salts or C 12 to C 44 dicarboxylic acids or their ammonium or alkali metal salts, F) optionally surfactants, G) optionally mono- or polyhydric alcohols, and H) no isocyanate-functional prepolymer having a weight fraction of low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol of below 1.0% by weight based on the prepolymer, obtainable by reaction of H1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol with H2) di- to hexafunctional polyalkylene oxides having an OH number of 22.5 to 112 mg KOH/g and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present, are provided, foamed and cured. A) hydrophilic polyisocyanates obtainable by reaction of A1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol and/or polyisocyanates obtainable therefrom with an isocyanate functionality of 2 to 6, with A2) monofunctional polyalkylene oxides having an OH number of 10 to 250, and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present, A1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol and/or polyisocyanates obtainable therefrom with an isocyanate functionality of 2 to 6, with A2) monofunctional polyalkylene oxides having an OH number of 10 to 250, and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present, B) heterocyclic 4-ring or 6-ring oligomers of low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol, C) water, D) optionally catalysts, E) optionally C 8 to C 22 monocarboxylic acids or their ammonium or alkali metal salts or C 12 to C 44 dicarboxylic acids or their ammonium or alkali metal salts, F) optionally surfactants, G) optionally mono- or polyhydric alcohols, and H) no isocyanate-functional prepolymer having a weight fraction of low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol of below 1.0% by weight based on the prepolymer, obtainable by reaction of H1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol with H2) di- to hexafunctional polyalkylene oxides having an OH number of 22.5 to 112 mg KOH/g and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present, H1) low molecular weight aliphatic diisocyanates having a molar mass of 140 to 278 g/mol with H2) di- to hexafunctional polyalkylene oxides having an OH number of 22.5 to 112 mg KOH/g and an ethylene oxide content of 50 to 100 mol% based on the total amount of oxyalkylene groups present,