The simple view of reading admits two components in accounting for individual differences in reading comprehension: a print-dependent component related to decoding and word identification, and a print-independent one related to oral language comprehension. It has been debated whether word or nonword reading is a better index of the print-dependent component and whether vocabulary measures fit within the print-independent component or constitute an additional factor. Here we apply a confirmatory factor analysis on a set of relevant measures from 488 Greek children in Grades 3–5 independently of reading comprehension. The results indicate that word and nonword reading do not constitute distinct factors but covary along the same two dimensions of accuracy and fluency. Oral vocabulary measures group with listening comprehension, resulting in excellent model fits. Strong correlations were observed between the latent factors of the purported print-dependent and print-independent components, consistent with an approach that focuses on the strong relations among semantic, orthographic, and phonological aspects of word representations.