Model checking techniques can be successfully employed as a test case generation technique to generate tests from formal models. The number of tests cases produced, however, is typically large for complex coverage criteria such as MCDC. Test-suite reduction can provide us with a smaller set of test cases that preserve the original coverage-often a dramatically smaller set. One potential drawback with test-suite reduction is that this might affect the quality of the test-suite in terms of fault finding. Previous empirical studies provide conflicting evidence on this issue. To further investigate the problem and determine its effect when testing formal models of software, we performed an experiment using a large case example of a Flight Guidance System, generated reduced test-suites for a variety of structural coverage criteria while preserving coverage, and recorded their fault finding effectiveness. Our results show that the size of the specification based test-suites can be dramatically reduced and that the fault detection of the reduced test-suites is adversely affected. In this report we describe our experiment, analyze the results, and discuss the implications for testing based on formal specifications.