A combustion turbine may have a cooling circuit for directing a cooling medium through the combustion turbine to cool various components of the combustion turbine. This cooling circuit may include a compressor, a combustor shell and a component of the combustion turbine to be cooled. This component may be a rotating blade of the combustion turbine. A pressure changing mechanism is disposed in the combustion turbine between the component to be cooled and the combustor shell. The cooling medium preferably flows from the compressor to the combustor shell, through a cooler, the component to the cooled and the pressure changing mechanism. After flowing through the pressure changing mechanism, the cooling medium is returned to the combustor shell. The pressure changing mechanism preferably changes the pressure of the cooling medium from a pressure at which it is exhausted from the component to be cooled to approximately that of the combustor shell.