Although mutation testing is one of the practical ways of enhancing test effectiveness in software testing, it could be sometimes infeasible in practical work for a large scale software so that the mutation testing becomes time-consuming and even in prohibited time. Therefore, the number of faults assumed to exist in the software under test should be reduced so as to be able to confine the time complexity of test within a reasonable period of time. This paper utilizes the concept of fault dominance and equivalence, which has long been employed 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 and become a feasible way of software testing. Examples and experimental results are presented to illustrate the effectiveness and the helpfulness of the technology proposed in the paper.