A process is described for removing acid gases from a gas stream in which an acid-gas-containing gas stream in which the sum of the partial pressures of the acid gases does not exceed 1,500 mbar is brought into contact with an aqueous absorbent in an absorption step and an absorbent is used which contains methyldiethanolamine and piperazine at a concentration of at least 8% by weight of the absorbent, an acid-gas-depleted gas stream and an acid-gas-loaded absorbent being obtained.