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This work is in line with the CoopFlow approach dedicated for workflow advertisement, interconnection, and cooperation in the context of virtual enterprises. To support cooperation, one has to deal with the partners' privacy respect. In fact, cooperation needs a certain degree of inter-visibility in order to perform interactions and data exchange. Nevertheless, cooperation may be employed as a cover to internalize the know-how of partners. To preserve privacy and autonomy, one must reduce workflow inter-visibility as tiny as the cooperation needs. We present in this paper a novel reduction-based method to preserve partners' privacy. The principle of the algorithm is to get rid of all activities as well as control and data flows that don't play any direct role into cooperation and don't affect the behavior of the original workflow.