Human fluid intelligence emerges from the interactions of various cognitive processes. Although some classic models characterize intelligence as a unitary "general ability," many distinct lines of research have suggested that it is possible to at least partially decompose intelligence into a set of subsidiary cognitive functions. Much of this work has focused on the relationship between intelligence and working memory, and more specifically between intelligence and the capacity-loading aspects of working memory. These theories focus on domain-general processing capacity limitations, rather than limitations specifically linked to working memory tasks. Performance on other capacity-constrained tasks, even those that have typically been given the label of "attention tasks," may thus also be related to fluid intelligence. We tested a wide range of attention and working memory tasks in 7- to 9-year-old children and adults, and we used the results of these cognitive measures to predict intelligence scores. In a set of 13 measures we did not observe a single "positive manifold" that would indicate a general-ability understanding of intelligence. Instead, we found that a small number of measures were related to intelligence scores. More specifically, we found two tasks that are typically labeled as "attentional measures", Multiple Object Tracking and Enumeration, and two tasks that are typically labeled as "working memory" measures, N-back and Spatial Span, were reliably related to intelligence. However, the links between attention and intelligence scores were fully mediated by working memory measures. In contrast, attention scores did not mediate the relations between working memory and intelligence. Furthermore, these patterns were indistinguishable across age groups, indicating a hierarchical cognitive basis of intelligence that is stable from childhood into adulthood.