Software testing is a critical part of software development. Test suite sizes may grow significantly with subsequent modifications to the software over time. Due to time and resource constraints for testing, test suite minimization techniques attempt to remove those test cases from the test suite that have become redundant over time since the requirements covered by them are also covered by other test cases in the test suite. Prior work has shown that test suite minimization techniques can severely compromise the fault detection effectiveness of test suites. In this paper, we present a novel approach to test suite reduction that attempts to selectively keep redundant tests in the reduced suites. We implemented our technique by modifying an existing heuristic for test suite minimization. Our experiments show that our approach can significantly improve the fault detection effectiveness of reduced suites without severely affecting the extent of test suite size reduction.