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Fault diagnosis processes consider the fact that a circuit fails a test as carrying more information than if the circuit passes a test. As a result, tests that detect smaller numbers of faults are likely to result in more accurate fault diagnosis. We study the existence of low-coverage tests, which detect small numbers of faults, for stuck-at faults, transition faults and path delay faults. The study shows that such tests are prevalent for path delay faults. We discuss the use of low-coverage tests for diagnosis of path delay faults, and describe a procedure for generating low-coverage tests for path delay faults.