A turbojet comprising a high-pressure compressor with several compression stages in which the pressure rises in a direction of air flow, from a low pressure to a high pressure, passing through intermediate pressures, and a system to bleed air in the turbojet and deliver the air to an air system. The bleeding system comprises a first air intake to bleed air at low pressure, a second air intake to bleed air at an intermediate pressure, a first valve and a second valve having inlets connected to the first air intake, a compressor having an inlet connected to the second valve outlet, a high-pressure valve connected to the second air intake, and a control valve connected to the air system, and a controller to control the opening and closing of the valves depending on the pressures at the first and second air intakes.