Are you right-brained or left-brained? The belief that individual cognitive differences may be characterized in terms of right or left hemispheric dominance is often accepted as conventional wisdom, but has never been clearly supported. Perhaps as a result, “normal neurocognition” has been almost invariably assumed to constitute one large homogenous group and modeled using a flat neuropsychological profile (i.e., using unimodal normal distributions across neuropsychological domains). The current project tested this assumption by exploring and characterizing heterogeneity in a cognitively healthy population. The neuropsychological profiles of cognitively-healthy individuals were characterized using latent profile analysis (LPA) on a normative dataset of the expanded Haltstead-Reitan neuropsychological Battery (eHRB). Participants were included that had been administered at least half of the eHRB measures with a memory test (N=982, age=20-85, education=7-20, 618 African-American, 364 Caucasian). The neurocognitive domains underlying performance on the eHRB were characterized and quantified using exploratory and confirmatory factor analyses on demographically-uncorrected eHRB test scores. Two series of LPAs were conducted on composite factor scores that were (1) corrected for demographics and (2) corrected for both demographics and general cognitive ability. Seven factors were identified: ‘working-memory’, ‘fluency’, ‘verbal episodic memory’, ‘language’, ‘visuospatial cognition’, ‘perceptual speed’, and ‘perceptual attention’. The first LPA revealed individual differences in general neurocognitive ability, with some individuals performing better than others across domains. After correcting for general neurocognitive ability, the second LPA revealed patterns of individual differences best described by four pairs of latent classes with opposite patterns of relative strengths and weaknesses. These patterns were characterized by tradeoffs along two dimensions: verbal-to-perceptual and analysis-to-attention/speed. When demographic characteristics are controlled, individual differences in normal neurocognition are dominated by general cognitive ability. At equivalent general cognitive ability, individual differences are characterized by relative tradeoffs along two almost orthogonal dimensions, verbal-to-perceptual and analysis-to-attention/speed. These findings suggest that different cognitive strategies or neuronal routes may be employed to attain similar general performance on neurocognitive testing. Based on brain function theories, these neuronal routes may involve differential activation of the left-versus-right cerebral hemispheres and of the ventral-versus-dorsal brain pathways, perhaps suggesting right- and left- but also top- and bottom-brained phenotypes.