Synchronous reluctance machines can be a viable solution in several applications, including high-speed ones. Their limitations in terms of power factor and torque density can be overcome by”assisting” the machine performance introducing permanent magnet (PM) materials within the rotor barriers. A standardized procedure for the design of this kind of machines for high-speed applications is still subject of numerous researches. Indeed, different criteria can be adopted for the PM-assistance and the final machine is clearly affected by the design choice. This paper proposes a hybrid approach for the design of high-speed permanent magnet assisted synchronous reluctance machines. The standard analytical procedure is improved by means of non-linear magnetic circuits useful to estimate the main flux components, whereas a quick FE-based refinement is used to correct the modeling inaccuracies. Then, the proposed routine is used to asses the power capability of this machine topology considering different design criteria for the permanent magnets placement and both low and high speed scenarios.