With the exponential growth in the number of transistors, not only test data volume and test application time may increase, but also multiple faults may exist in one chip. Test compaction has been a de-facto design-for-testability technique to reduce the test cost. However, the compacted test responses make multiple-fault diagnosis rather difficult. When there is no space compactor, the most likely suspect fault is considered producing the failing responses most similar to the failing responses observed from the automatic test equipment. But when compactor exists, those suspect faults may no longer have the same high possibility of being the actual faults. To address this problem, we introduce a novel metric explanation necessity. By using both of the new metric and the traditional metric explanation capability, we evaluate the possibility of a suspect fault to be the actual fault. For ISCAS'89 and ITC'99 benchmark circuits equipped with extreme space compactors, experimental results show that 98.8% of the top-ranked suspect faults hit the actual faults, outperforming a previous work by 11.3%.