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Earlier research results have shown that for many designs, a large portion of path delay faults is not robustly testable. In this paper, we investigate the test strategy for the non-robustly testable faults. We first present some experimental results to show that the quality of a non-robust test set may be very poor in detecting small delay defects caused by manufacturing process variation. We further show that a better set of non-robust tests can be obtained by including timing information in test generation. A good non-robust test can tolerate a larger timing variation on the off-inputs of the path than a poor test. An algorithm for generating such better quality non-robust tests is presented. We present experimental results to compare quality of non-robust test sets with and without using our method. We also present an algorithm, as well as experimental results, for generating validatable non-robust tests.