Word list reading fluency is theoretically expected to depend on single word reading speed. Yet the correlation between the two diminishes with increasing fluency, while fluency remains strongly correlated to serial digit naming. We hypothesized that multi-element sequence processing is an important component of fluency. We used confirmatory factor analyses with serial and discrete naming tasks with matched items, including digits, dice, objects, number words, and words, performed by about 100 Greek children in each of Grades 1, 3, and 5. Separable serial and discrete factors emerged across grades, consistent with distinct skill dimensions. Loadings were greater for serial than discrete, suggesting that discrete processing does not fully determine serial processing. Average serial performance differed more than discrete between grades, consistent with improvement beyond single-item speed. Serial word reading aligned increasingly with the serial factor at higher grades. Thus, word reading fluency is gradually dominated by skill in simultaneously processing multiple successive items through different stages (termed "cascading"), beyond automatization of individual words.