Abstract: A method for obtaining an acid gas stream having a pressure of from 3 to 30 bar by removal of the acid gases from a liquid stream comprising as impurities H2S and if appropriate other acid gases, the molar fraction of H2S, based on the total amount of acid gases, being at least 50 mol %, which comprises a) in at least one absorption step, bringing the fluid stream into intimate contact with a liquid absorption medium and thus producing a fluid stream substantially freed from acid gases and an acid-gas-loaded liquid absorption medium (step a), b) separating from one another the fluid stream substantially freed from acid gases and the acid-gas-loaded liquid absorption medium (step b), c) separating, by heating and if appropriate expansion or stripping, the acid-gas-loaded liquid absorption medium into an acid gas stream having a pressure of from 3 to 30 bar and a regenerated liquid absorption medium (step c) d) passing the regenerated liquid absorption medium into a heat exchanger and cooling it there, by using