It is often thought that an agent may be held morally responsible for bringing about a negative outcome only if they could have done otherwise. Inspired by previous research linking moral judgment to free will ascriptions and representations of possibility, the present work asks whether the reverse is true: Does bringing about a negative outcome make preferable alternatives appear more possible? In a two-alternative forced-choice experiment (N = 317), we manipulated the moral character of the victim of a traffic accident, and asked participants under soft time pressure whether bystanders had a series of alternative possibilities to save the victim. Our pre-registered analyses revealed that preventing a fatal accident was perceived as slightly less possible, and acknowledging these alternative possibilities demanded more time, when the victim was evil than when the victim was neutral or morally good. Fitting a hierarchical drift diffusion model, we uncovered that this asymmetry was largely explained by the bias (or z) parameter, and not the drift rate (or v parameter): When considering alternative courses of action that would have saved a wrongdoer’s life, the starting point of the evidence accumulation process was biased toward impossibility–relative to the good and neutral victim conditions. The rate of evidence accumulation, by contrast, was similar across experimental conditions. In sum, our study found modest evidence that moral valence influences the construal of alternative possibilities and illustrated how the application of drift diffusion modeling to questions in moral psychology may offer novel insights beyond the analysis of responses and reaction times.