A method for treating a gas mixture containing acid gases, including: contacting the gas mixture with an absorbing solution, to obtain a de-acidified gas mixture and an absorbing solution with acid gases. To regenerate the absorbing solution with acid gases, the absorbing solution is passed into a first regenerator at a first pressure, then the solution is passed into a second regenerator at a second pressure, and finally to a third regenerator at a third pressure, the third pressure being less than the second pressure which is less than the first pressure. The gases from the second and third regenerator are compressed and recycled to the first and second regenerator, respectively. Gases from the second and/or the third regenerator are drawn off to provide a gas mixture rich in hydrogen sulfide. Gases from the first regenerator are drawn off to provide a gas mixture rich in carbon dioxide.