A method of operating a pneumatic system for an aircraft, the aircraft having a gas turbine engine, the gas turbine engine comprising one or more core compressors (14, 16) and a bypass fan, the pneumatic system comprising: a handling bleed offtake operating by an engine controller in accordance with a predetermined schedule to ensure that the respective core compressor (14, 16) does not stall or surge during operation, a high pressure cabin bleed offtake and a low pressure cabin bleed offtake, each forming a second core compressor bleed offtake (132, 134), and each controllable by respective modulation valves (135, 133) and configured to respectively provide bleed flows from the gas turbine core compressor (14, 16); and a turbocompressor comprising an air compressor mechanically driven by an air turbine; wherein a first core compressor bleed offtake is in fluid communication with the turbocompressor air turbine to thereby drive the air turbine, and the second core compressor bleed offtake (132, 134) is in fluid communication with the turbocompressor air compressor such that air from the second core compressor bleed offtake (132, 134) is compressed by the turbocompressor air compressor; characterised in that the method comprises determining whether the low pressure cabin bleed offtake pressure is above a predetermined value and, where the low pressure cabin bleed offtake pressure is above the predetermined value: operating the respective modulation valves (135, 133) to open the low pressure cabin bleed offtake and close the high pressure bleed offtake; and where the low pressure cabin bleed offtake pressure is determined not to be above the predetermined value, the method comprises determining whether an engine handling bleed valve is open and, where the engine handling bleed valve is determined to be open, operating the respective valves (133, 135) to open the high pressure cabin bleed offtake, and where the engine handling bleed valve is determined to be closed, operating the respective valve (133, 135) to open the high pressure cabin bleed offtake and operating the respective valve to open the handling bleed offtake. a handling bleed offtake operating by an engine controller in accordance with a predetermined schedule to ensure that the respective core compressor (14, 16) does not stall or surge during operation, a high pressure cabin bleed offtake and a low pressure cabin bleed offtake, each forming a second core compressor bleed offtake (132, 134), and each controllable by respective modulation valves (135, 133) and configured to respectively provide bleed flows from the gas turbine core compressor (14, 16); and a turbocompressor comprising an air compressor mechanically driven by an air turbine; wherein a first core compressor bleed offtake is in fluid communication with the turbocompressor air turbine to thereby drive the air turbine, and the second core compressor bleed offtake (132, 134) is in fluid communication with the turbocompressor air compressor such that air from the second core compressor bleed offtake (132, 134) is compressed by the turbocompressor air compressor; characterised in that the method comprises determining whether the low pressure cabin bleed offtake pressure is above a predetermined value and, where the low pressure cabin bleed offtake pressure is above the predetermined value: operating the respective modulation valves (135, 133) to open the low pressure cabin bleed offtake and close the high pressure bleed offtake; and where the low pressure cabin bleed offtake pressure is determined not to be above the predetermined value, the method comprises determining whether an engine handling bleed valve is open and, where the engine handling bleed valve is determined to be open, operating the respective valves (133, 135) to open the high pressure cabin bleed offtake, and where the engine handling bleed valve is determined to be closed, operating the respective valve (133, 135) to open the high pressure cabin bleed offtake and operating the respective valve to open the handling bleed offtake.