Single-phase flux reversal motors (FRMs) with sintered rare-earth permanent magnets on the stator for low-cost high-speed applications have a reliable rotor and a good specific power. However, to reduce eddy current loss, the sintered rare-earth magnets on the stator have to be segmented into several pieces and their cost increases with the number of magnet segments. An alternative to the sintered magnets can be bonded magnets, in which eddy current loss is almost absent. The remanence of bonded magnets is lower than that of sintered magnets, and they are prone to demagnetization. However, the cost of low-power motors with bonded magnets can be lower because of the simpler manufacturing technology and the lower material cost. This paper discusses various aspects of the optimal design of FRM with bonded magnets, applying the Nelder–Mead method. An objective function for optimizing an FRM with bonded magnets is designed to ensure the required efficiency, reduce torque oscillations, and prevent the bonded magnets from demagnetizing. As a result, it is shown that the FRM with bonded magnets has approximately the same efficiency as the FRM with sintered magnets. In addition, the peak-to-peak torque ripple is minimized and the minimal instantaneous torque is maximized.