Some examinees' test-taking behavior may be so idiosyncratic that their scores are not comparable to the scores of more typical examinees. Appropriateness indices, which provide quantitative measures of response-pattern atypicality, can be viewed as statistics for testing a null hypothesis of normal test-taking behavior against an alternative hypothesis of atypical behavior. Performance curves and the performance envelope are introduced as devices for obtaining a least upper bound for the power of the most powerful statistical tests for aberrance. The performance envelope of a set of tests is the function on (0,1) whose value at t is the least upper bound of the hit rates of the tests when their false positive rate is t. The performance curve of an appropriateness index is the performance envelope of the tests for aberrance based on the index. For some testing anomalies, it is possible to determine the performance envelope for the set of all statistical tests for aberrance, and to identify a test whose performance curve is identical to this performance envelope. An algorithm for computing optimal tests is described. Its use is illustrated with data simulated from the verbal section of the scholastic aptitude test. (Author/GDC)