An electro-impedance tomography (EIT) system (2), with a computing unit (4) and a respirator (1) is described for gentle mechanical lung ventilation especially in case of atelectases. The presence, the extent and/or the spatial distribution of atelectases is detected by the EIT system (2) and sent to the respirator (1) so that the respiration pressure is increased step by step by the respirator (1) until the current image of the lung status corresponds to a first status image of healthy lungs or comes close to it with minimal deviations. The respiration pressure is subsequently reduced again step by step by the respirator (1) until the computing unit (4) detects a reduction of the ventilated lung areas and the respiration pressure is subsequently increased again by means of the respirator (1) to the last value at which no change occurred in the ventilated lung areas.