Parametrization of rotor topology in synchronous reluctance machines (SynRM), particularly those with circular flux barriers, has been explored through two distinct approaches. The one with a classic model offers limited parameters, constraining design flexibility, while the other with a complete model of non-concentric barriers provides extensive design freedom at the cost of increased parameters to be optimized and potential superfluous geometries. It is essential to find a fast and effective way for rotor parametrization besides these two approaches. In this paper, a new rotor parametrization method is proposed, based on partly-concentric circular flux barriers and an equation revealed between key parameters. It exhibits a design freedom between the classic model with concentric flux barriers and the complete model with non-concentric ones. A simple but efficient equation is introduced to enlarge the parameter scan range while avoiding useless and unfeasible rotor geometries, making the method more time-efficient. The three methods are adopted to parameterize and optimize a same SynRM. Predesigned end angles of the flux barriers are introduced in the integer-slot machines to help reduce the number of parameters while maintaining a high optimization performance. At last, the performances of the optimized machines obtained from the three models are compared, validating the fastness and effectiveness of the proposed design methodology.