Purpose: Aphasia is a language disorder caused by acquired brain injury, which generally involves difficulty naming objects. Naming ability is assessed by measuring picture naming, and models of naming performance have mostly focused on accuracy and excluded valuable response time (RT) information. Previous approaches have therefore ignored the issue of processing efficiency, defined here in terms of optimal RT cutoff, that is, the shortest deadline at which individual people with aphasia produce their best possible naming accuracy performance. The goals of this study were therefore to (a) develop a novel model of aphasia picture naming that could accurately account for RT distributions across response types; (b) use this model to estimate the optimal RT cutoff for individual people with aphasia; and (c) explore the relationships between optimal RT cutoff, accuracy, naming ability, and aphasia severity. Method: A total of 4,021 naming trials across 10 people with aphasia were scored for accuracy and RT onset. Data were fit using a novel ex-Gaussian multinomial RT model, which was then used to characterize individual optimal RT cutoffs. Results: Overall, the model fitted the empirical data well and provided reliable individual estimates of optimal RT cutoff in picture naming. Optimal cutoffs ranged between approximately 5 and 10 s, which has important implications for assessment and treatment. There was no direct relationship between aphasia severity, naming RT, and optimal RT cutoff. Conclusion: The multinomial ex-Gaussian modeling approach appears to be a promising and straightforward way to estimate optimal RT cutoffs in picture naming in aphasia. Limitations and future directions are discussed.