In a method for removing acid gases from a fluid stream, the fluid stream, which is in contact with an absorption medium within an absorber, is passed through a first absorption zone in the absorber to remove a majority of acid gases from the fluid stream. The fluid stream is susequently passed through a second absorption zone in the absorber to further remove acid gases from the fluid stream. The loaded absorption medium is passed into a first regeneration zone to obtain a partially regenerated absorption medium, and a part of the partially regenerated absorption medium is passed into the first absorption zone. The other part of the partially regenerated absorption medium is passed into a second regeneration zone to obtain a regenerated absorption medium. A part of the regenerated absorption medium is passed into the first absorption zone and the other part is passed into the second absorption zone.