Supine sleeping, recommended to prevent sudden infant death, should be started in the delivery hospital, but meets concern that neonates may exhibit more intermittent hypoxia in this position. We aimed to demonstrate that intermittent hypoxia is equally rare in supine and side position. We enrolled 609 term neonates in a crossover study. Pulse oximeter saturation (Spo2) was recorded throughout; feeding periods were excluded. The rate of desaturation events to <80%/h was the primary study variable. Four hundred seventy-six recordings fulfilled study criteria. Mean duration of recording was 4.8 h in side and 4.9 h in supine position (SD 0.8 for both). There was a mean of 0.11 desaturation events per hour in supine and 0.05 per hour in side position. Of the 118 infants with desaturation events, more had such events only in supine position (64 vs. 31 infants). For supine compared with side position, the adjusted odds ratio for at least one desaturation event was 2.0 (95% confidence interval 1.3–3.1). The lowest Spo2 value reached during these events was 56% in supine and 53% in side position. These neonates had more desaturation events while sleeping supine. We speculate, however, that this positional effect likely is too small to affect outcome.