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Generation of n-detection test sets is typically done for a single fault model. This paper investigates the generation of n-detection test sets by pairing each fault of a target fault model with n faults of a different fault model. Tests are generated such that they detect both faults of a pair. To facilitate test generation, the faults included in a single pair are selected such that they have overlapping requirements for their detection. The advantage of this approach is that it ensures the detection of additional faults that would not be targeted during the n-detection test generation process for a single fault model. Experimental results with transition faults as the first fault model and four-way bridging faults as the second fault model are presented.