Airplanes and jet engines are provided that includes an engine compressor; a combustor in flow communication with the engine compressor; an engine turbine in flow communication with the combustor to receive combustion products from the combustor; and a bleed air cooling system in fluid communication with bleed air from the engine compressor. The bleed air cooling system can include a first precooler in fluid communication with the bleed air from the engine compressor; a cooling system turbine in fluid communication with and downstream from the first precooler; and a discharge conduit from the cooling system turbine that is configured to be in fluid communication with at least one of an aircraft thermal management system and an aircraft environmental control system. Methods are also described for providing cooling fluid from a jet engine.