We used structural equation modeling to investigate sources of individual differences in oral reading fluency in a transparent orthography, Russian. Phonological processing, orthographic processing, and rapid automatized naming were used as independent variables, each derived from a combination of two scores: phonological awareness and pseudoword repetition, spelling and orthographic choice, and rapid serial naming of letters and digits, respectively. The contribution of these to oral text-reading fluency was evaluated as a direct relationship and via two mediators, decoding accuracy and unitized reading, measured with a single-word oral reading test. The participants were “good” and “poor” readers, i.e., those with reading skills above the 90th and below the 10th percentiles (n = 1344, grades 2–6, St. Petersburg, Russia). In both groups, orthographic processing skills significantly contributed to fluency and unitized reading, but not to decoding accuracy. Phonological processing skills did not contribute directly to reading fluency in either group, while contributing to decoding accuracy and, to a lesser extent, to unitized reading. With respect to the roles of decoding accuracy and unitized reading, the results for good and poor readers diverged: in good readers, unitized reading, but not decoding accuracy, was significantly related to reading fluency. For poor readers, decoding accuracy (measured as pseudoword decoding) was related to reading fluency, but unitized reading was not. These results underscore the importance of orthographic skills for reading fluency even in an orthography with consistent phonology-to-orthography correspondences. They also point to a qualitative difference in the reading strategies of good and poor readers.