Removing CO2 and, if necessary, H2S from gases

CO2 and, if necessary, H2S are removed from a gas which contains CO2 and may contain H2S with an absorption liquid by a process in which the gas which contains CO2 and may contain H2S is treated in an absorption zone with the absorption liquid, the treated gas is removed from the absorption zone, the absorption liquid which is obtained from the absorption zone and is laden with CO2 and may be laden with H2S is then regenerated in that the said absorption liquid is let down in one or more let-down stages and a let-down gas is taken off at the top of the first let-down stage or, in the case of a plurality of let-down stages, at the top of one or more of the first to penultimate let-down stages, and the partially regenerated absorption liquid obtained from the last let-down stage is, if required, fed to a stripping zone for further regeneration, one or more acid gas streams which contain the CO2 and may contain H2S being removed from the regeneration stage and the regenerated absorption liquid being recycled to the absorption zone, wherein a bleed stream of completely or partially regenerated absorption liquid is fed to one or more of the let-down stages from which the let-down gas is removed, at a point above the feed of the absorption liquid to be let down.