A process for producing flexible polyurethane foams, in which a) polyisocyanate prepolymer is mixed with b) polymeric compounds having groups reactive toward isocyanates, c) optionally chain extenders and/or crosslinkers, d) catalyst, e) blowing agent comprising water and f) optionally additives to give a reaction mixture and reacted to give the flexible polyurethane foam, wherein the polyisocyanate prepolymers (a) have an NCO content of from 16 to 30% by weight, based on the total weight of the component a), and are obtainable by reacting a1) diphenylmethane diisocyanate comprising a1a) diphenylmethane 2,4'-diisocyanate, a1b) diphenylmethane 4,4'-diisocyanate and a1c) higher homologues of diphenylmethane diisocyanate having more than two rings with a2) polyols comprising a2a) ethylene-oxide-rich polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of at least 55% by weight and a2b) low-ethylene oxide polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of not more than 20% by weight and where the proportion of a1a) diphenylmethane 2,4'-diisocyanate is from 5 to 15% by weight and that of a1b) diphenylmethane 4,4'-diisocyanate is from 40 to 80% by weight, based on the total weight of the polyisocyanates a1), and the polymeric compounds (b) having groups which are reactive toward isocyanates comprise b1) from 60 to 80% by weight of at least one polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of from 55 to 95% by weight, b2) from 20 to 30% by weight of at least one polyalkylene oxide having a hydroxyl number of from 20 to 80 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of from 0 to 40% by weight and where the proportion of the compounds b1) and b2), based on the total weight of the polymeric compounds (b) having groups which are reactive toward isocyanates, is at least 80% by weight. a) polyisocyanate prepolymer is mixed with b) polymeric compounds having groups reactive toward isocyanates, c) optionally chain extenders and/or crosslinkers, d) catalyst, e) blowing agent comprising water and f) optionally additives a1) diphenylmethane diisocyanate comprising a1a) diphenylmethane 2,4'-diisocyanate, a1b) diphenylmethane 4,4'-diisocyanate and a1c) higher homologues of diphenylmethane diisocyanate having more than two rings with a2) polyols comprising a2a) ethylene-oxide-rich polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of at least 55% by weight and a2b) low-ethylene oxide polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of not more than 20% by weight and b1) from 60 to 80% by weight of at least one polyalkylene oxide having a hydroxyl number of from 20 to 60 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of from 55 to 95% by weight, b2) from 20 to 30% by weight of at least one polyalkylene oxide having a hydroxyl number of from 20 to 80 mg KOH/g derived from one or more bifunctional to tetrafunctional starter molecules and a proportion of ethylene oxide units, based on the total weight of alkylene oxide units, of from 0 to 40% by weight