Systems with three (or more) free parameters are considered. Pre-determined locations are assigned to one pair of complex roots, and their existence is guaranteed by assigning two degrees of freedom (two parameters) to constrain them to the desired location. The constraints are used to construct a reduced characteristic equation from which the assigned parameters have been eliminated. The polynomial thus obtained defines the locations of all roots except the specified complex pair, and (for the case of three parameters) a root locus study permits choice of a value of the third parameter such that the root pattern is compatible with a dominance requirement for the specified complex pair