We describe a framework for randomized unit testing, and give empirical evidence that generating unit test cases randomly and then minimizing the failing test cases results in significant benefits. Randomized generation of unit test cases (sequences of method calls) has been shown to allow high coverage and to be highly effective. However, failing test cases, if found, are often very long sequences of method calls. We show that Zeller and Hildebrandt?s test case minimization algorithm significantly reduces the length of these sequences. We study the resulting benefits qualitatively and quantitatively, via a case study on found open-source data structures and an experiment on lab-built data structures.