Nested models confirmatory factor analysis was used to compare a higher-order and hierarchical model of human cognitive ability structure. In a higher-model the effects of g on observed subtest scores are completely mediated by lower-order, more specific ability factors. In a hierarchical model, the effects of both g and specific abilities on observed subtest scores are direct and independent. In two batteries of 20 and 21 cognitive tests taken from the Minnesota Study of Twins Reared Apart, the hierarchical model was better fitting than the higher-order model. Although g was by far the stronger influence on cognitive performance, there were important specific ability influences on cognitive performance independent of this. To avoid conflating these independent influences, the adoption of a hierarchical measurement model for empirical investigations in human cognitive abilities is recommended. Analyses also suggested that comparisons of higher-order and hierarchical analyses should involve comparisons of local fit criteria and not just rely on global fit statistics. This is because unmodelled complexity can potentially introduce biases into comparisons of the higher-order and hierarchical modal that are not discernable using only global fit statistics.