Test suite minimization techniques attempt to reduce the cost of saving and reusing tests during software maintenance, by eliminating redundant tests from test suites. A potential drawback of these techniques is that in minimizing a test suite, they might reduce the ability of that test suite to reveal faults in the software. A recent study showed that minimization can reduce test suite size without significantly reducing the fault detection capabilities of test suites. To further investigate this issue, we performed an experiment in which we compared the costs and benefits of minimizing test suites of various sizes for several programs. In contrast to the previous study, our results reveal that the fault-detection capabilities of test suites can be severely compromised by minimization.