A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.