A process for separating off acid gases from a water-comprising fluid stream wherein the water-comprising fluid stream is contacted in an absorption zone with an absorbent, producing a deacidified fluid stream and an acid gas-loaded absorbent; the deacidified fluid stream is contacted in a scrubbing zone with an aqueous scrubbing liquid, producing a deaminated, deacidified fluid stream and an amine-loaded scrubbing liquid which is cooled, producing an absorber top condensate; the loaded absorbent is passed into a desorption zone producing a regenerated absorbent and desorbed acid gases; the regenerated absorbent is returned to the absorption zone in order to form an absorbent circuit, to which the amine-loaded scrubbing liquid and the absorber top condensate are introduced; and the desorbed acid gases are conducted through an enrichment zone and the acid gases exiting at the top of the enrichment zone are cooled, producing a desorber top condensate.