Fatigue has been implicated in an alarming number of motor vehicle accidents, costing billions of dollars and thousands of lives. Unfortunately, the ability to predict performance impairments in complex task domains like driving is limited by a gap in our understanding of the explanatory mechanisms. In this paper, we describe an attempt to generate a priori predictions of degradations in driver performance due to sleep deprivation. We accomplish this by integrating an existing account of the effect of sleep loss and circadian rhythms on sustained attention performance with a validated model of driver behavior. Although quantitative empirical data for validation are lacking, the predicted results across four days of sleep deprivation match qualitative trends published in the literature, and illustrate the potential for making useful predictions of performance in naturalistic task contexts that are relevant to real applied problems.