It is demonstrated that at high altitude the performance of a tail-controlled aerodynamic missile can degrade because of the existence of low frequency right-half plane zeroes in the airframe transfer function when either proportional navigation or optimal guidance is used. A new guidance law that accounts for the airframe zeroes is developed numerically and shown to have superior performance to existing guidance laws at the higher altitudes. Although no closed-form solution for the guidance law is presented, the resultant numerical values for the control gains of the guidance law can easily be stored as a multidimensional table in existing on-board flight control computers. Two methodologies for computing the guidance law control gains are presented.