Process for preparing a polyoxyalkylene polyol 1) by reacting at least one H-functional starter compound with at least one alkylene oxide, comprising the following steps: i) providing a component A) comprising a polyoxyalkylene polyol A1) having a calculated OH number (OHN A1) of 600 to 1060 mg KOH/g and a neutral or acidic salt of an inorganic Brønsted acid by i-1) reacting an H-functional starter compound with one or more alkylene oxides B1) using a basic catalyst, i-2) reacting the mixture resulting from i-1) with a Brønsted acid having a pKa < 1, ii) subsequently reacting component A) with one or more alkylene oxides B2) in the presence of a DMC catalyst, where ii-1) the component A) resulting from step i) is admixed with a DMC catalyst and stripped at a temperature T S of not more than 145°C and ii-2) the mixture resulting from ii-1) is reacted with one or more alkylene oxides B2) to give a polyoxyalkylene polyol 1), where the quotient of the reaction temperature T R and the alkylene oxide metering rate A R, defined as the percentage of the mass of alkylene oxide to be metered in in step ii) which is metered in per hour, is T R / A R < 5.9 h * ° C / % and wherein the OH number of the polyoxyalkylene polyol 1) obtained after performance of step ii) is ≥ 200 mg KOH/g. i) providing a component A) comprising a polyoxyalkylene polyol A1) having a calculated OH number (OHN A1) of 600 to 1060 mg KOH/g and a neutral or acidic salt of an inorganic Brønsted acid by i-1) reacting an H-functional starter compound with one or more alkylene oxides B1) using a basic catalyst, i-2) reacting the mixture resulting from i-1) with a Brønsted acid having a pKa < 1, i-1) reacting an H-functional starter compound with one or more alkylene oxides B1) using a basic catalyst, i-2) reacting the mixture resulting from i-1) with a Brønsted acid having a pKa < 1, ii) subsequently reacting component A) with one or more alkylene oxides B2) in the presence of a DMC catalyst, where ii-1) the component A) resulting from step i) is admixed with a DMC catalyst and stripped at a temperature T S of not more than 145°C and ii-2) the mixture resulting from ii-1) is reacted with one or more alkylene oxides B2) to give a polyoxyalkylene polyol 1), where the quotient of the reaction temperature T R and the alkylene oxide metering rate A R, defined as the percentage of the mass of alkylene oxide to be metered in in step ii) which is metered in per hour, is T R / A R < 5.9 h * ° C / % and wherein the OH number of the polyoxyalkylene polyol 1) obtained after performance of step ii) is ≥ 200 mg KOH/g. ii-1) the component A) resulting from step i) is admixed with a DMC catalyst and stripped at a temperature T S of not more than 145°C and ii-2) the mixture resulting from ii-1) is reacted with one or more alkylene oxides B2) to give a polyoxyalkylene polyol 1), where the quotient of the reaction temperature T R and the alkylene oxide metering rate A R, defined as the percentage of the mass of alkylene oxide to be metered in in step ii) which is metered in per hour, is T R / A R < 5.9 h * ° C / % and wherein the OH number of the polyoxyalkylene polyol 1) obtained after performance of step ii) is ≥ 200 mg KOH/g.