A turbine engine includes a compressor, and high and low pressure turbines. The configuration includes a mid-compression station which can be, in the case of a single compressor in the middle of that compressor, or at the exit of the first compressor in the case of two compressors. Also, there is an exit pressure station at the exit of the compression system. A first gas flow line is interposed between the mid-compression station of the compressor and the low pressure turbine, and a second gas flow line is interposed between the exit pressure station of the compression system and the high pressure turbine. A first valve is coupled to the first gas flow line and modulates a low pressure flow rate of coolant in the first gas flow line, and a second valve is coupled to the second gas flow line and modulates a high pressure flow rate of coolant in the second coolant flow line. A controller is configured to operate the first and second valves based on an operating condition of the turbine engine so as to improve the specific fuel consumption while ensuring acceptable stall margin.