Miller (1956) identified his famous limit of 7 plus or minus 2 items based in part on absolute identification--the ability to identify stimuli that differ on a single physical dimension, such as lines of different length. An important aspect of this limit is its independence from perceptual effects and its application across all stimulus types. Recent research, however, has identified several exceptions. We investigate an explanation for these results that reconciles them with Miller's work. We find support for the hypothesis that the exceptional stimulus types have more complex psychological representations, which can therefore support better identification. Our investigation uses data sets with thousands of observations for each participant, which allows the application of a new technique for identifying psychological representations: the structural forms algorithm of Kemp and Tenenbaum (2008). This algorithm supports inferences not possible with previous techniques, such as multidimensional scaling. (Contains 2 tables and 2 figures.)