A method of operating a bleed air system comprising: providing air from a first source at a first temperature and a first pressure through a first inlet; providing air from a second source at a second temperature and a second pressure through a second inlet, wherein the second temperature and the second pressure are higher than the first pressure and the first temperature; characterised in that the method further comprises: providing air from a third source at a third temperature and a third pressure, wherein the third temperature is lower than either of the first temperature and the second temperature and the third pressure is lower than either of the first pressure or the second pressure; directing airflow from one of the first inlet or the third source to a compressor portion of a turbocompressor with a third control valve; directing airflow exhausted from the compressor portion back to the second source through a first control valve; directing airflow to a turbine portion of the turbocompressor from one of the first inlet, the second inlet and an outlet of the compressor portion with one of the first control valve, a second control valve and a high pressure shutoff valve; directing an output airflow from a turbine outlet of the turbine portion through an outlet passage to an aircraft system (70, 72); and selectively directing air to bypass the turbine portion with a flow control valve through a bypass passage to mix with the output airflow from the turbine outlet into the outlet passage. providing air from a first source at a first temperature and a first pressure through a first inlet; providing air from a second source at a second temperature and a second pressure through a second inlet, wherein the second temperature and the second pressure are higher than the first pressure and the first temperature; characterised in that the method further comprises: providing air from a third source at a third temperature and a third pressure, wherein the third temperature is lower than either of the first temperature and the second temperature and the third pressure is lower than either of the first pressure or the second pressure; directing airflow from one of the first inlet or the third source to a compressor portion of a turbocompressor with a third control valve; directing airflow exhausted from the compressor portion back to the second source through a first control valve; directing airflow to a turbine portion of the turbocompressor from one of the first inlet, the second inlet and an outlet of the compressor portion with one of the first control valve, a second control valve and a high pressure shutoff valve; directing an output airflow from a turbine outlet of the turbine portion through an outlet passage to an aircraft system (70, 72); and selectively directing air to bypass the turbine portion with a flow control valve through a bypass passage to mix with the output airflow from the turbine outlet into the outlet passage. providing air from a third source at a third temperature and a third pressure, wherein the third temperature is lower than either of the first temperature and the second temperature and the third pressure is lower than either of the first pressure or the second pressure; directing airflow from one of the first inlet or the third source to a compressor portion of a turbocompressor with a third control valve; directing airflow exhausted from the compressor portion back to the second source through a first control valve; directing airflow to a turbine portion of the turbocompressor from one of the first inlet, the second inlet and an outlet of the compressor portion with one of the first control valve, a second control valve and a high pressure shutoff valve; directing an output airflow from a turbine outlet of the turbine portion through an outlet passage to an aircraft system (70, 72); and selectively directing air to bypass the turbine portion with a flow control valve through a bypass passage to mix with the output airflow from the turbine outlet into the outlet passage.