An absorbent for the selective removal of hydrogen sulfide from a fluid stream comprising carbon dioxide and hydrogen sulfide, wherein the absorbent contains an aqueous solution, comprising: a) an amine or a mixture of amines of the general formula (I) wherein R1 is C1-C5-alkyl; R2 is C1-C5-alkyl; R3 is selected from hydrogen and C1-C5-alkyl; x is an integer from 2 to 10; and b) an ether or a mixture of ethers of the general formula (II): R4—[O—CH2—CH2]y—OH; wherein R4 is C1-C5-alkyl; and y is an integer from 2 to 10; wherein R1 and R4 are identical; wherein the mass ratio of b) to a) is from 0.08 to 0.5. The absorbent is suitable for the selective removal of hydrogen sulfide from a fluid stream comprising carbon dioxide and hydrogen sulfide. 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 is easily obtainable.