A method for obtaining an acid gas stream having a pressure of from 5 to 30 bar by removal of the acid gases from a liquid stream comprising as impurities H 2 S and optionally other acid gases, the molar fraction of H 2 S, 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 chemical absorption medium selected from the group consisting of - solutions consisting principally of aliphatic or cycloaliphatic amines having from 2 to 12 carbon atoms, alkanolamines having from 2 to 12 carbon atoms, cyclic amines where 1 or 2 nitrogen atoms, together with 1 or 2 alkanediyl groups, form 5-, 6- or 7-membered rings, mixtures of the abovementioned solutions, aqueous solutions of the abovementioned mixtures and solutions, - aqueous solutions comprising salts of amino acids - aqueous potash solutions which optionally comprise piperazine or monoethanolamine - aqueous NaOH solution or milk of lime, 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 optionally expansion or stripping, the acid-gas-loaded liquid absorption medium into an acid gas stream having a pressure of from 5 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 a part of its thermal energy to heat up the acid-gas-loaded liquid absorption medium in step (c) (step d) e) recirculating the regenerated liquid absorption medium to step a) (step e). a) in at least one absorption step, bringing the fluid stream into intimate contact with a liquid chemical absorption medium selected from the group consisting of - solutions consisting principally of aliphatic or cycloaliphatic amines having from 2 to 12 carbon atoms, alkanolamines having from 2 to 12 carbon atoms, cyclic amines where 1 or 2 nitrogen atoms, together with 1 or 2 alkanediyl groups, form 5-, 6- or 7-membered rings, mixtures of the abovementioned solutions, aqueous solutions of the abovementioned mixtures and solutions, - aqueous solutions comprising salts of amino acids - aqueous potash solutions which optionally comprise piperazine or monoethanolamine - aqueous NaOH solution or milk of lime, and thus producing a fluid stream substantially freed from acid gases and an acid-gas-loaded liquid absorption medium (step a), - solutions consisting principally of aliphatic or cycloaliphatic amines having from 2 to 12 carbon atoms, alkanolamines having from 2 to 12 carbon atoms, cyclic amines where 1 or 2 nitrogen atoms, together with 1 or 2 alkanediyl groups, form 5-, 6- or 7-membered rings, mixtures of the abovementioned solutions, aqueous solutions of the abovementioned mixtures and solutions, - aqueous solutions comprising salts of amino acids - aqueous potash solutions which optionally comprise piperazine or monoethanolamine - aqueous NaOH solution or milk of lime, 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 optionally expansion or stripping, the acid-gas-loaded liquid absorption medium into an acid gas stream having a pressure of from 5 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 a part of its thermal energy to heat up the acid-gas-loaded liquid absorption medium in step (c) (step d) e) recirculating the regenerated liquid absorption medium to step a) (step e).