To ascertain whether cerebral lateralities can be considered aptitudes or individual difference measures within an aptitude-treatment-interaction (ATI) framework, hemispheric asymmetries and cognitive psychometric tests were administered to 50 right-handed, Caucasian, male Navy recruits. Principal factor analysis with varimax rotation was computed for these measures. A major portion of the variability in the data was attributed to cerebral lateralities either acting independently or interactively with cognitive attributes. Their proven construct validity and importance as individual difference indices suggest that hemispheric asymmetries can be considered "aptitudes" within an ATI context. However, a number of conceptual problems, in addition to methodological difficulties, may limit the pedagogical payoff from ATI and asymmetry research. A four-page reference list is included. (Author/LMM)