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We investigate a new fault ordering heuristic for test generation in full-scan circuits. The heuristic is referred to as the accidental detection index. It associates a value ADI(f) with every circuit fault f. The heuristic estimates the number of faults that will be detected by a test generated for f. Fault ordering is done such that a fault with a higher accidental detection index appears earlier in the ordered fault set and targeted earlier during test generation. This order is effective for generating compact test sets, and for obtaining a test set with a steep fault coverage curve. Such a test set has several applications. We present experimental results to demonstrate the effectiveness of the heuristic.