Giftedness, like other rare phenomena, is often explained by principles beyond those used to explain the normal variation of mental ability. Before parsimony is abandoned and additional principles are invoked, the following five points should be considered. (1) Gifted samples often have restricted ranges, reducing correlations with intelligence and making standard tests insensitive to relationships that may exist. Though this is an obvious point, it is frequently overlooked. (2) Theories of intelligence that view g as a single global ability are inadequate. Intelligence is better seen as a complex system of independent but interrelated parts. Measures of g are global ratings of system functioning, but global measures do not explain mental ability in terms of either more basic cognitive abilities or underlying brain functioning. More basic explanations of intelligence are essential for understanding giftedness. (3) Correlations among intellectual abilities are lowest for persons of high intelligence. Specific skills will be less highly correlated among the gifted. (4) Heritability of cognitive abilities may differ across the intelligence range, though evidence on this point is mixed. (5) Achievement and intelligence are different things. Discrepancies between intelligence and achievement are due to environment. Such a finding is consistent with the idiosyncratic development of giftedness.