Optimal appropriateness indices, recently introduced by Levine and Drasgow (1984), provide the highest rates of detection of aberrant response patterns that can be obtained from item responses. These optimal appropriateness indices are used to study three important problems in appropriateness measurement. First, the maximum detection rates of two particular forms of aberrance are determined for a long unidimensional test. These detection rates are shown to be moderately high. Second, two versions of the standardized "L sub 0" appropriateness index are compared to optimal indices. At low false alarm rates one standardized "L sub 0" index has detection rates that are about 65 percent as large as optimal for spuriously high (cheating) test scores. However, for the spuriously low scores expected from persons with ill-advised testing strategies or reading problems, both standardized "L sub 0" indices are far from optimal. Finally, detection rates for polychotomous and dichotomous scorings of the item responses are compared. It is shown that dichotomous scoring causes serious decreases in the detectability of some aberrant response patterns. Consequently, appropriateness measurement constitutes one practical testing problem where significant gains result from the use of a polychotomous item response model. (Author/LMO)