The purpose of this study was to contrast three models of the RAN-reading relationship derived from the most prominent theoretical accounts of how RAN is related to reading: the phonological processing, the orthographic processing and the speed of processing accounts. Grade 4 Greek-speaking children (n = 208; 114 girls, 94 boys; mean age = 117.29 months) were administered measures of general cognitive ability, RAN, phonological processing, orthographic processing, speed of processing, and reading fluency. Phonological processing and orthographic processing were assessed with both accuracy and speeded measures. Structural equation modeling showed that the most parsimonious model was one in which RAN predicted reading fluency directly and through orthographic processing. Phonological processing did not predict reading fluency and speed of processing was more important for the RAN-orthographic/phonological processing relationships than for the RAN-reading relationship. Taken together, these findings suggest that what is unique to RAN is more important for the prediction of reading fluency than what it shares with either speed of processing, phonological processing, or orthographic processing.