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In Petri-net (PN) modeling of flexible manufacturing systems, deadlock prevention is often addressed by means of siphon-control methods. Constraints that avoid the emptying of siphons can be easily implemented using additional places suitably connected to the PN transitions. Efficient siphon-based techniques achieve highly permissive solutions using as few control places as possible. One such technique employs a set-covering approach to optimally match emptiable siphons to critical markings. In this paper, a modified version of the method is proposed that achieves the same results in terms of permissivity and size of the control subnet but avoids full siphon enumeration. This greatly reduces the overall computational time and memory requirements and allows the applicability of the method to large-size models.