A method for obtaining an acid gas stream having a pressure of from 3 to 30 bar by removal of acid gases from a fluid stream containing H.sub.2S, the molar fraction of H.sub.2S based on the total amount of acid gases being at least 50 mol %, the method comprising bringing the fluid stream into intimate contact with a liquid absorption medium, thus producing a fluid stream substantially freed from acid gases and an acid-gas-loaded liquid absorption medium; separating the fluid stream and the liquid absorption medium; separating, by heating and optionally by expansion or stripping, the liquid absorption medium into an acid gas stream and a regenerated liquid absorption medium; passing the regenerated liquid absorption medium into a heat exchanger and cooling it there by using part of its thermal energy to heat up the acid-gas-loaded liquid absorption medium; and recirculating the regenerated liquid absorption medium.