Executive function (EF) is related to reading. However, there is a lack of clarity around (a) the relative contribution of different components of EF to different reading components (word reading, fluency, comprehension), and (b) how EF operates in the context of known strong language predictors (e.g., components of the simple view of reading or SVR), and other skills theoretically related to reading (e.g., vocabulary, processing speed) and/or to EF (e.g., short-term memory, motor function). In a large sample of 3rd to 5th graders oversampled for struggling readers, this paper evaluates the impact of EF derived from a bifactor model (Cirino, Ahmed, Miciak, Taylor, Gerst, & Barnes, 2018) in the context of well-known covariates and demographics. Beyond common EF, five specific factors (two related to working memory, and factors of fluency, self-regulated learning, and behavioral inattention/metacognition) were addressed. EF consistently showed a unique contribution to already-strong predictive models for all reading outcomes; for reading comprehension, EF interacted with SVR indices (word reading and listening comprehension). The findings extend and refine our understanding of the contribution of EF to reading skill.