A series of multiobjective 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 multiobjective H-infinity design problems, based on a number of different types of sensitivity problem, 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 similar techniques can be used to incorporate simultaneous specifications for different control objectives such as H-2, l(1) etc., for the sensitivities. The approach is illustrated by an experimental set-up for a steel mill test rig.