The synchronous reluctance machines with transversally laminated rotor and multi flux barriers per pole reach a high torque density, so that they are proposed as a valid alternative to permanent magnet machines. Such machines have been analyzed for different applications, mainly home appliance, industrial tool, traction, up to low-speed high-power generators. On the contrary, the use of synchronous reluctance machines for high-speed applications remains almost unexplored yet. The aim of this paper is to investigate the potential of a high-speed synchronous reluctance machine. An optimization is carried out so as to maximize the machine performance (high power, proper power factor, low vibration) at a given speed. The machine size is fixed and the focus is on the rotor geometry, with the purpose of maximizing the electromagnetic torque, according to the necessary thickness of the ribs. It is shown that, even if the ribs are thick, it is possible to reach a proper torque density. It is shown that different solutions exist, which allow to reach high torque and minimum torque ripple. However, the optimal solutions are quite sensitive to the geometrical variations, so that a particular care is required in the manufacturing of the machine. Finally, the power limit of the synchronous reluctance motor with barrier rotor is found.