Sleep restriction causes impaired cognitive performance that can result in adverse consequences in many occupational settings. Individuals may rely on self-perceived alertness to decide if they are able to adequately perform a task. It is therefore important to determine the relationship between an individual's self-assessed alertness and their objective performance, and how this relationship depends on circadian phase, hours since awakening, and cumulative lost hours of sleep. Healthy young adults (aged 18-34) completed an inpatient schedule that included forced desynchrony of sleep/wake and circadian rhythms with twelve 42.85-hour "days" and either a 1:2 (n = 8) or 1:3.3 (n = 9) ratio of sleep-opportunity: enforced-wakefulness. We investigated whether subjective alertness (visual analog scale), circadian phase (melatonin), hours since awakening, and cumulative sleep loss could predict objective performance on the Psychomotor Vigilance Task (PVT), an Addition/Calculation Test (ADD) and the Digit Symbol Substitution Test (DSST). Mathematical models that allowed nonlinear interactions between explanatory variables were evaluated using the Akaike Information Criterion (AIC). Subjective alertness was the single best predictor of PVT, ADD, and DSST performance. Subjective alertness alone, however, was not an accurate predictor of PVT performance. The best AIC scores for PVT and DSST were achieved when all explanatory variables were included in the model. The best AIC score for ADD was achieved with circadian phase and subjective alertness variables. We conclude that subjective alertness alone is a weak predictor of objective vigilant or cognitive performance. Predictions can, however, be improved by knowing an individual's circadian phase, current wake duration, and cumulative sleep loss.