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This paper studies how details of a particular model can effect the efficacy of a search for detects. We find that if the test method is fixed, we can identity classes of software that are more or less testable. Using a combination of model mutators and machine learning, we find that we can isolate topological features that significantly change the effectiveness of a defect detection tool. More specifically, we show that for one defect detection tool (a stochastic search engine) applied to a certain representation (finite state machines), we can increase the average odds of finding a defect from 69% to 91%. The method used to change those odds is quite general and should apply to other defect detection tools being applied to other representations.