In Yan et al. (J Inf Sci Eng 25(1): 167-183, 2009), a deadlock prevention policy is proposed for a subclass of Petri nets, (SPMR)-P-3, that can well model a large class of flexible manufacturing systems (FMS) where deadlocks are caused by unmarked siphons in their Petri net models. To validate the effectiveness and efficiency of the proposed approach, two examples were demonstrated in Yan et al. (J Inf Sci Eng 25(1): 167-183, 2009). This paper shows that there is a problem with one of the control places computed for one of the examples. In Yan et al. (J Inf Sci Eng 25(1): 167-183, 2009), for another example, two different deadlock prevention supervisors were proposed. It is also shown in this paper that, for these two supervisors, it is possible to obtain two subsets of control places. Thus, the structures of the two supervisors are further simplified with the same permissive system behaviours.