An absorbent for the selective removal of hydrogen sulfide over carbon dioxide from a fluid stream, wherein the absorbent contains an aqueous solution, comprising an amine of formula (I) and/or an amine of formula (II) wherein U—V—W is CH—O—CHR5, N—CO—CHR5 or N—CO—NR5; U′—V′—W is C—O—CR5; R1 is independently C1-C5-alkyl; R2 is selected from hydrogen and C1-C5-alkyl; R3 is independently selected from hydrogen and C1-C5-alkyl; R4 is independently selected from hydrogen and C1-C5-alkyl; R5 is selected from hydrogen, C1-C5-alkyl, (C1-C5-alkoxy)-C1-C5-alkyl, and hydroxy-C1-C5-alkyl; and x is an integer from 1 to 10. The absorbent has a reduced tendency for phase separation at temperatures falling within the usual range of regeneration temperatures for the aqueous amine mixtures and a low volatility in aqueous solvents.