The standard model is that word identification in reading is a holistic process, most efficient when words are centered in the visual field. In contrast, rational models of reading predict word identification to be a constructive process, where readers efficiently gather visual information about a word, and may combine visual information about different parts of the word obtained across multiple fixations to identify it. We tease apart these accounts by arguing that rational models should predict that the most efficient place in a word to make a second fixation (refixation) depends on the visual information the reader has already obtained.We present evidence supporting this prediction from an eye movement corpus. Computational model simulations confirm that a rational model predicts this finding, but a model implementing holistic identification does not. These results suggest that refixations can be well understood as rationally gathering visual information, and that word identification works constructively.