An important question in software testing is whether it is reasonable to apply coverage based criteria as a lter to reduce the size of a test set. An empirical study was conducted using a test set minimization technique to explore the eeect of reducing the size of a test set, while keeping block coverage constant, on the fault detection strength of the resulting minimized test set. Two types of test sets were examined. For those with respect to a xed size, no test case screening was conducted during the generation, whereas for those with respect to a xed coverage, each subsequent test case had to improve the overall coverage in order to be included. The study reveals that no matter how a test set is generated (with or without any test case screening) block minimized test sets have a size/eeectiveness advantage, in terms of a signiicant reduction in test set size but with almost the same fault detection eeectiveness, over the original non-minimized test sets.