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We demonstrate that undetectable single stuck-at faults in full-scan benchmark circuits tend to cluster in certain areas. This implies that certain areas may remain uncovered by a test set for single stuck-at faults. We describe an extension to the set of target faults aimed at providing a better coverage of the circuit in the presence of undetectable single stuck-at faults. The extended set of target faults consists of double stuck-at faults that include an undetectable fault as one of their components. The other component is a detectable fault adjacent to the undetectable fault. We present experimental results of fault simulation and test generation for the extended set of target faults.