Although Mutation is one of the practical ways of enhancing the effectiveness of the test cases to be applied to an application under test, it could be sometimes infeasible for there being too many assumed faults and mutants to be operated in a larger scale system so that the mutation operating becomes time-consuming and even prohibited. Therefore, the number of faults assumed to exist in the software under test should be reduced. Fault Collapsing is a common way of reducing the number of faults in hardware testing. However, this strategy can now be well implanted into the area of software testing. In this paper, we utilize the concept of fault dominance and equivalence, which has long been used in hardware testing, for revealing a novel way of reducing the number of faults assumed to hide in software systems. Once the number of faults assumed in software is decreased sharply, the effectiveness of mutation testing will be greatly enhanced. Examples and experimental results are presented to illustrate the effectiveness and the helpfulness of the technology proposed in the paper.