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Faster-than-at-speed testing is an effective approach to screen small delay defects (SDDs) and increase test quality and in-field reliability. This paper presents a novel framework of faster-than-at-speed test to minimize the slack of the sensitized path for each fault. The basic strategy is to use multiple faster-than-at-speed test timings with endpoint masking for each pattern. By performing a detailed analysis of the sensitized path delay for active faults and active endpoints in each pattern, we can minimize the slack for the detectable faults while preventing a large increase in pattern count. We also present methods to maximize the sensitized path delay and further reduce the pattern count under a constraint on the allowable slack size, instead of minimizing the slack. Experimental results for ITC'99 benchmark circuits show the effectiveness of the proposed methods in terms of slack size and sensitized path delay for detectable faults, statistical delay quality level (SDQL) and pattern count.