Test case prioritization techniques schedule test cases for execution in an order that attempts to maximize some objective function. A variety of objective functions are applicable; one such function involves rate of fault detection --- a measure of how quickly faults are detected within the testing process. An improved rate of fault detection during regression testing can provide faster feedback on a system under regression test and let debuggers begin their work earlier than might otherwise be possible. In this paper, we describe several techniques for prioritizing test cases and report our empirical results measuring the effectiveness of these techniques for improving rate of fault detection. The results provide insights into the tradeoffs among various techniques for test case prioritization.