Relationships between complex memory span, simple memory span, phonological awareness tasks, and beginning reading were investigated. Seven-year-olds were administered two complex span tasks, two simple span tasks, and four phonological awareness tasks. Relationships between the tasks were assessed, as well as their predictive importance with regard to reading accuracy, reading comprehension, and arithmetic. Correlations revealed that three of the four phonological awareness tasks were highly correlated with one another and with both of the complex span tasks. Regression analyses showed that the phonological awareness and reading-related complex span scores accounted for unique and shared portions of the variance in all three cognitive abilities, while the arithmetic-related complex span scores only made a significant unique contribution to the variance in arithmetic. Finally, simple memory span scores only explained significant portions of the variance in any of the cognitive abilities when entered first into the regression equations. The results suggested that phonological awareness and complex span tasks make a shared and a unique contribution to the variance in all three cognitive abilities, questioning Daneman and Carpenter's (1980, 1983) domain-specific hypothesis.