Stroke is a leading cause of disability, and language impairments (aphasia) after stroke are both common and particularly feared. Most stroke survivors with aphasia exhibit anomia (difficulties with naming common objects), but while many therapeutic interventions for anomia have been proposed, treatment effects are typically much larger in some patients than others. Here, we asked whether that variation might be more systematic, and even predictable, than previously thought. 18 patients, each at least 6 months after left hemisphere stroke, engaged in a computerised treatment for their anomia over a 6-week period. Using only: (a) the patients' initial accuracy when naming (to-be) trained items; (b) the hours of therapy that they devoted to the therapy; and (c) whole-brain lesion location data, derived from structural MRI; we developed Partial Least Squares regression models to predict the patients' improvements on treated items, and tested them in cross-validation. Somewhat surprisingly, the best model included only lesion location data and the hours of therapy undertaken. In cross-validation, this model significantly out-performed the null model, in which the prediction for each patient was simply the mean treatment effect of the group. This model also made promisingly accurate predictions in absolute terms: the correlation between empirical and predicted treatment response was 0.62 (95% CI 0.27, 0.95). Our results indicate that individuals' variation in response to anomia treatment are, at least somewhat, systematic and predictable, from the interaction between where and how much lesion damage they have suffered, and the time they devoted to the therapy.