Sojourners to high altitude often experience poor sleep quality due to sleep-disordered breathing. Additionally, multiple aspects of cognitive function are impaired at high altitude. However, the impact of acclimatization on sleep-disordered breathing and whether poor sleep is a major contributor to cognitive impairments at high altitude remains uncertain. We conducted nocturnal actigraphy and polygraphy, as well as daytime cognitive function tests, in 15 participants (33% women) at sea level and over 3 days of partial acclimatization to high altitude (3800 m). Our goal was to determine if sleep-disordered breathing improved over time and if sleep-disordered breathing was associated with cognitive function. The apnea-hypopnea index and oxygen desaturation index increased on night 1 (adj. p = 0.026 and adj. p = 0.026, respectively), but both improved over the subsequent 2 nights. These measures were matched by poorer self-reported sleep quality on the Stanford Sleepiness Scale and PROMIS questionnaires following 1 night at high altitude (adj. p = 0.027 and adj. p = 0.022, respectively). The reaction time on the psychomotor vigilance task was slower at high altitude and did not improve (SL: 199 ± 27, ALT1: 224 ± 33, ALT2: 216 ± 41, ALT3: 212 ± 27 ms). The reaction times on the balloon analog risk task decreased at high altitude (SL: 474 ± 235, ALT1: 375 ± 159, ALT2: 291 ± 102, ALT3: 267 ± 90 ms), perhaps indicating increased risk-taking behavior. Finally, multiple cognitive function measures were associated with sleep-disordered breathing and measures of subjective sleep quality, rather than low daytime arterial oxygen saturation. These data indicate that sleep-disordered breathing at moderately high altitude improves with partial acclimatization and that some aspects of cognitive performance in unacclimatized sojourners may be impacted by poor sleep rather than hypoxemia alone.