This study explored four hypotheses: (a) the relationships among rapid automatized naming (RAN) and processing speed (PS) to irregular word, non-word, and word reading; (b) the predictive power of various RAN and PS measures, (c) the cognitive correlates that best predicted irregular word, non-word, and word reading, and (d) reading performance of typical and poor readers on irregular word, non-word, and word reading. Sixty participants in Grades 1-4 with and without reading disabilities were administered a measure of phonological awareness (PA) and a measure of working memory (WM), and several measures of RAN and PS. The findings indicated that PS had the strongest correlation with irregular word reading, whereas RAN had the strongest correlations with word reading and non-word reading. As with previous research RAN letters was the best predictor of reading skills. The best model for predicting reading was based on a combined measure of PA and RAN letters. An interesting finding was that the correlation between irregular and non-word reading was significant for students with typical reading, but insignificant for the poor readers. These findings provide support for both the dual-route and double-deficit theory of dyslexia that ascribes independent contributions of PA and RAN to the development of reading skills. (Contains 6 tables.)