Light-induced improvements in alertness are more prominent during nighttime than during the day, suggesting that alerting effects of light may depend on internal clock time or wake duration. Relative contributions of both factors can be quantified using a forced desynchrony (FD) designs. FD designs have only been conducted under dim light conditions (<10 lux) since light above this amount can induce non-uniform phase progression of the circadian pacemaker (also called relative coordination). This complicates the mathematical separation of circadian clock phase from homeostatic sleep pressure effects. Here we investigate alerting effects of light in a novel 4 × 18 h FD protocol (5 h sleep, 13 h wake) under dim (6 lux) and bright light (1300 lux) conditions. Hourly saliva samples (melatonin and cortisol assessment) and 2-hourly test sessions were used to assess effects of bright light on subjective and objective alertness (electroencephalography and performance). Results reveal (1) stable free-running cortisol rhythms with uniform phase progression under both light conditions, suggesting that FD designs can be conducted under bright light conditions (1300 lux), (2) subjective alerting effects of light depend on elapsed time awake but not circadian clock phase, while (3) light consistently improves objective alertness independent of time awake or circadian clock phase. Reconstructing the daily time course by combining circadian clock phase and wake duration effects indicates that performance is improved during daytime, while subjective alertness remains unchanged. This suggests that high-intensity indoor lighting during the regular day might be beneficial for mental performance, even though this may not be perceived as such.