Adaptive Random Testing subsumes a class of algorithms that detect the first failure with less test cases than Random Testing. The present paper shows that a "reference method" in the field of Adaptive Random Testing is not effective for higher dimensional input domains and clustered failure-causing inputs. The reason for this behavior is explained, and a modified method is proposed and analyzed. Categories and Subject Descriptors D.2.5 [Software Engineering]: Testing and Debugging-Testing tools; G.3 [Probability and Statistics]: Reliability and life testing General Terms Algorithms, Reliability, Verification Keywords Adaptive Random Testing, Random Testing, Test case selection