Mathematical models designed to predict alertness or performance have been developed primarily as tools for evaluating work and/or sleep-wake schedules that deviate from the traditional daytime orientation. In general, these models cope well with the acute changes resulting from an abnormal sleep but have difficulties handling sleep restriction across longer periods. The reason is that the function representing recovery is too steep--usually exponentially so--and with increasing sleep loss, the steepness increases, resulting in too rapid recovery. The present study focused on refining the Three-Process Model of alertness regulation. We used an experiment with 4 h of sleep/night (nine participants) that included subjective self-ratings of sleepiness every hour. To evaluate the model at the individual subject level, a set of mixed-effect regression analyses were performed using subjective sleepiness as the dependent variable. These mixed models estimate a fixed effect (group mean) and a random effect that accounts for heterogeneity between participants in the overall level of sleepiness (i.e., a random intercept). Using this technique, a point was sought on the exponential recovery function that would explain maximum variance in subjective sleepiness by switching to a linear function. The resulting point explaining the highest amount of variance was 12.2 on the 1-21 unit scale. It was concluded that the accumulation of sleep loss effects on subjective sleepiness may be accounted for by making the recovery function linear below a certain point on the otherwise exponential function.