In this paper, the static-state feedback stabilization problem is considered for a class of single-input linear systems so that the closed-loop eigenvalues are as insensitive as possible to unstructured perturbations, Given a pair of complex conjugate numbers gamma,gamma* and a closed and bounded interval Gamma of the real axis sufficiently far to the left of such a pair, a procedure for the design of a static-state feedback is given so that the closed-loop system has gamma, gamma* as the dominant pair of complex conjugate eigenvalues, while all the other eigenvalues are distinct and belong to Gamma, with the sum of the squares of the condition numbers taking the minimum value.