The effects of properties of words on their reading aloud response times (RTs) are 1 major source of evidence about the reading process. The precision with which such RTs could potentially be predicted by word properties is critical to evaluate our understanding of reading but is often underestimated due to contamination from individual differences. We estimated this precision without such contamination individually for 4 people who each read 2,820 words 50 times each. These estimates were compared to the precision achieved by a 31-variable regression model that outperforms current cognitive models on variance-explained criteria. Most (around 2/3) of the meaningful (non-first-phoneme, non-noise) word-level variance remained unexplained by this model. Considerable empirical and theoretical-computational effort has been expended on this area of psychology, but the high level of systematic variance remaining unexplained suggests doubts regarding contemporary accounts of the details of the mechanisms of reading at the level of the word. Future assessment of models can take advantage of the availability of our precise participant-level database.