Adelman, Marquis, Sabatos-DeVito, and Estes (2013) collected word naming latencies from 4 participants who read 2,820 words 50 times each. Their recommendation and practice was that R2 targets set for models should take into account subject idiosyncrasies as replicable patterns, equivalent to a subjects-as-fixed-effects assumption. In light of an interaction involving subjects, they broke down the interaction into individual subject data. Courrieu and Rey's (2015) commentary argues that (a) single-subject data need not be more reliable than subject-average data, and (b) anyway, treating groups of subjects as random samples leads to valid conclusions about general mechanisms of reading. Point (a) was not part of Adelman et al.'s claim. In this reply, we examine the consequences of using the fixed-effect assumption. It (a) produces the correct target to check if by-items regression models contain all necessary variables, (b) more accurately constrains cognitive models, (c) more accurately reveals general mechanisms, and (d) can offer more powerful tests of effects. Even when individual differences are not the primary focus of a study, the fixed-effect analysis is often preferable to the random-effects analysis.