A gas turbine engine (100; 150; 170) comprising: a compressor section having a downstream most end and a cooling air tap at a location spaced upstream from said downstream most end, air from said cooling air tap being passed through at least one boost compressor (118; 152) and at least one heat exchanger (124; 130), and then passed to a turbine section to cool said turbine section, said boost compressor (118; 152) being controlled to provide a desired pressure to said turbine section; characterised by: further comprising a mixing chamber that receives air downstream of said boost compressor (118; 152) and selectively receives air from a second location which has been compressed by said compressor section to a pressure higher than a pressure of said cooling air tap, wherein said mixing chamber is configured to control a mixture of said airflow downstream of said boost compressor (118; 152), and said airflow from said second location to selectively deliver a mixture of the airflows to said turbine section, wherein: said boost compressor (118; 152) is controlled by a controlled tap downstream of said cooling air tap, and also upstream from said downstream most end, wherein a control is configured to control the flow of air from said controlled tap to said at least one heat exchanger (124, 130); said boost compressor is provided with a controllable output, and said boost compressor is provided with a variable area inlet, wherein said variable area inlet includes the ability to adjust at least one of a vane and throat geometry to change the volume of air passing to said boost compressor; or the engine further comprises a take-off shaft driven by a turbine which drives at least a portion of said compressor section configured to drive a gearbox to, in turn, drive said boost compressor (118, 152) and a transmission and/or differential positioned between said gearbox and said boost compressor to control the speed of said boost compressor. a compressor section having a downstream most end and a cooling air tap at a location spaced upstream from said downstream most end, air from said cooling air tap being passed through at least one boost compressor (118; 152) and at least one heat exchanger (124; 130), and then passed to a turbine section to cool said turbine section, said boost compressor (118; 152) being controlled to provide a desired pressure to said turbine section; characterised by: further comprising a mixing chamber that receives air downstream of said boost compressor (118; 152) and selectively receives air from a second location which has been compressed by said compressor section to a pressure higher than a pressure of said cooling air tap, wherein said mixing chamber is configured to control a mixture of said airflow downstream of said boost compressor (118; 152), and said airflow from said second location to selectively deliver a mixture of the airflows to said turbine section, wherein: said boost compressor (118; 152) is controlled by a controlled tap downstream of said cooling air tap, and also upstream from said downstream most end, wherein a control is configured to control the flow of air from said controlled tap to said at least one heat exchanger (124, 130); said boost compressor is provided with a controllable output, and said boost compressor is provided with a variable area inlet, wherein said variable area inlet includes the ability to adjust at least one of a vane and throat geometry to change the volume of air passing to said boost compressor; or the engine further comprises a take-off shaft driven by a turbine which drives at least a portion of said compressor section configured to drive a gearbox to, in turn, drive said boost compressor (118, 152) and a transmission and/or differential positioned between said gearbox and said boost compressor to control the speed of said boost compressor. said boost compressor (118; 152) is controlled by a controlled tap downstream of said cooling air tap, and also upstream from said downstream most end, wherein a control is configured to control the flow of air from said controlled tap to said at least one heat exchanger (124, 130); said boost compressor is provided with a controllable output, and said boost compressor is provided with a variable area inlet, wherein said variable area inlet includes the ability to adjust at least one of a vane and throat geometry to change the volume of air passing to said boost compressor; or the engine further comprises a take-off shaft driven by a turbine which drives at least a portion of said compressor section configured to drive a gearbox to, in turn, drive said boost compressor (118, 152) and a transmission and/or differential positioned between said gearbox and said boost compressor to control the speed of said boost compressor.