A series of multi objective H-infinity design problems are considered in this paper. The problems are formulated as a number of coupled H-infinity design problems. These H-infinity problems can be formulated as sensitivity problems, complementary sensitivity problems, or control sensitivity problems for every output (or input) in the system. It turns out that these multi objective H-infinity design problems, based on a number of different types of sensitivity problems, can be exactly decoupled into k H-infinity sensitivity problems for stable systems, where k is the number of outputs (for unstable systems, independent stabilization is required). Further, it is shown how to use similar techniques to incorporate simultaneous specifications for different control objectives such as H-two, L-one, etc., for the sensitivities. The approach is illustrated by an experimental setup for a steel mill test rig