Since the PF scheduling algorithm[13], which is optimal in the hard real-time multiprocessor environments, several scheduling algorithms have been proposed. All these algorithms assume the fixed unit quantum size, and this assumption has problems in the mode change environments. To settle the problem, we already proposed a method for deciding the optimal quantum size[2]. In this paper, we propose improved methods considering the task set whose utilization e is less than or equal to p/3+1. As far as the numbers of computations used to determine the optimal quantum size are concerned, newly proposed methods are proved to be more efficient than our previous ones.