An absorbent for selective removal of hydrogen sulfide over carbon dioxide from a fluid stream, comprising an aqueous solution comprising: a) a tertiary amine of the general formula in which R 1 is a C 2-4 -hydroxyalkyl and R 2 and R 3 are each independently selected from C 1-3 -alkyl and C 2-4 -hydroxyalkyl; b) an aminic pH promoter, the aminic pH promoter being selected from compounds of the general formula in which R 4 is selected from hydrogen; OR 7 in which R 7 is selected from hydrogen and C 1-4 -alkyl; and NR 8 R 9 in which R 8 and R 9 are each independently selected from C 1-5 -alkyl and C 2-5 -hydroxyalkyl; R 5 and R 6 are each independently selected from C 1-5 -alkyl and C 2-5 -hydroxyalkyl; and of the general formula in which R 10 is selected from C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino) -C 1-5 -alkyl; R 11 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; R 12 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl;and R 13 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; and x is an integer from 2 to 4; where the molar ratio of b) to a) is in the range from 0.05 to 1.0; and c) an acid having a pK A of less than 6 in such an amount that the pH of the aqueous solution measured at 120°C is 7.9 to less than 8.8. a) a tertiary amine of the general formula in which R 1 is a C 2-4 -hydroxyalkyl and R 2 and R 3 are each independently selected from C 1-3 -alkyl and C 2-4 -hydroxyalkyl; b) an aminic pH promoter, the aminic pH promoter being selected from compounds of the general formula in which R 4 is selected from hydrogen; OR 7 in which R 7 is selected from hydrogen and C 1-4 -alkyl; and NR 8 R 9 in which R 8 and R 9 are each independently selected from C 1-5 -alkyl and C 2-5 -hydroxyalkyl; R 5 and R 6 are each independently selected from C 1-5 -alkyl and C 2-5 -hydroxyalkyl; and of the general formula in which R 10 is selected from C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino) -C 1-5 -alkyl; R 11 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; R 12 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl;and R 13 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; and x is an integer from 2 to 4; where the molar ratio of b) to a) is in the range from 0.05 to 1.0; and R 10 is selected from C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino) -C 1-5 -alkyl; R 11 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; R 12 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl;and R 13 is selected from C 1-5 -alkyl, C 1-5 -aminoalkyl, C 2-5 -hydroxyalkyl and (di-C 1-4 -alkylamino)-C 1-5 -alkyl; and x is an integer from 2 to 4; where the molar ratio of b) to a) is in the range from 0.05 to 1.0; and c) an acid having a pK A of less than 6 in such an amount that the pH of the aqueous solution measured at 120°C is 7.9 to less than 8.8.