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Test sets for path delay faults in circuits with large numbers of paths are typically generated for path delay faults associated with the longest circuit paths. It is shown that such test sets may not detect faults associated with the next-to-longest paths. This may lead to undetected failures since shorter paths may fail without any of the longest paths failing. In addition, paths that appear to be shorter may actually be longer than the longest paths if the procedure used for estimating path length is inaccurate. A test enrichment procedure is proposed that increases significantly the number of faults associated with the next-to-longest paths that are detected by a test set without increasing its size. This is achieved by targeting both types of faults, but ensuring that the test generation procedure would detect the faults associated with the longest paths, while allowing the procedure the flexibility of detecting or not detecting the faults associated with the next-to-longest paths. The proposed procedure thus improves the quality of the test set without increasing its size. The test enrichment procedure is built on top of a new and effective dynamic test compaction procedure in order to demonstrate that test enrichment is effective even for compact test sets.