Increased real-time risk-taking under sleep loss could be marked by changes in risk perception or acceptance. Risk-perception processes are those involved in estimating real-time parameters such as the speeds and distances of hazardous objects. Risk-acceptance processes relate to response choices given risk estimates. Risk-taking under fatigue was studied using a simulated intersection-crossing driving task in which subjects decided when it was safe to cross an intersection as an oncoming car approached from the cross street. The subjects performed this task at 3-hour intervals over a 36-hour period without sleep. Results were modeled using a model of real-time risky decision making that has perceptual components that process speed, time and distance information, and a decisional component for accepting risk. Results showed that varying a parameter for the decisional component across sessions best accounted for variations in performance relating to time of day.