A non-smooth optimization approach for designing constant output-feedback controllers for linear time-invariant systems with lightly damped poles is considered. The design requirements combine H∞ performance requirements with regional pole constraints excluding high frequency lightly damped poles. In contrast to the usual (full) pole-placement (FPP) problem, the problem dealt here is one of Selective Pole Placement (SPP). The latter design problem is frequently encountered in the control of aircraft with non-negligible aeroelastic modes which are too fast to be handled by the control surface actuators. As in the FPP case, the pole constraints are embedded in the design criterion using a transformation on the system model which modifies the H ∞-norm. of the closed-loop system via a barrier function that is related to the closed-loop poles damping. In The SPP case, however, numerical calculations of the gradient of the cost function are needed rather than a closed form solution derived for the FPP. The method is applied to a flight control example of a flexible aircraft.