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In many multimedia applications, some faults induce errors that are user-imperceptible and thus are acceptable. By not testing for these faults, the effective yield can be significantly increased based on the principle of error-tolerance. However, studies have shown that test patterns generated by a conventional ATPG procedure targeting only unacceptable faults also detect many acceptable faults, resulting in a significant degradation in achievable yield improvement. In this paper we present a multi-phase test technique that can perfectly prevent this over-detection problem. Solid theoretical derivations are provided to validate the effectiveness of this technique. Compared with previous work, only a much smaller number of test patterns are required and thus the required test cost can be much lower. Experimental results on benchmark circuits illustrate the high efficiency of this novel technique.