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In this paper, we deal with the deadlock prevention problem in a new class of nets, ES3PR, where deadlocks are related to unmarked siphons. The major disadvantage of the existing approaches is that too many monitors and arcs have to be added. In our deadlock prevention approach, strict minimal siphons are divided into elementary and dependent ones. For each elementary siphon, a monitor is added to prevent it from being emptied without generating emptiable control-induced siphons. The controllability of the dependent siphons is ensured by changing the control depth variables of related elementary siphons, which leads to the liveness of the supervisor for the plant model. Finally, the application of the approach is illustrated with an FMS example.