Assume that an initial stabilizing controller K-0(s), which satisfies various closed loop frequency domain specifications, has been a priori synthesized using, e.g. H-infinity control, mu synthesis techniques or closed loop convex synthesis. Remembering that the order of K-0(s) is typically at least equal to the order of the plant to be controlled, the aim of this paper is to find a stabilizing reduced order controller, which also satisfies the performance specifications and which moreover minimizes the open loop bandwidth. To this aim, the structured singular value mu is used to translate at each frequency closed loop frequency domain specifications into requirements on the frequency response of the controller. The principle of our reduction method is thus very close to the original idea of the SISO QFT design approach, except that the problem of translating closed loop frequency domain specifications into open loop ones is much more complex in the MIMO case. The problem reduces to the issue of finding a controller, whose frequency response belongs at each frequency to a template. The convexity of these templates greatly facilitates the practical realization of the controller. As a final point, the method is successfully applied to a standard H-infinity problem, which is extracted from the mu Analysis and Synthesis Toolbox of Matlab, namely the synthesis of an autopilot for the space shuttle.