Summary: This paper presents a numerical investigation of an optimal re-entry manoeuvre under several control and control-state constraints. The essential aim of the optimization is the minimization of the maximal skin temperature of an orbiter. It is demonstrated that the interaction of different solution techniques is indispensable in order to successfully treat such a highly constrained problem. The reduction of the skin temperature is significant. Moreover, the maximum heat flux and the integrated heat flux are also reduced considerably by the optimization.