Official accident and traffic density statistics on Swedish highways were used to compute the relative risk (Odds Ratio - OR) of being injured or killed in a traffic accident at different times of day. After removing accidents due to alcohol 10344 accidents remained for computations, and the period 10:00h-11:00h was used as the reference point. The highest total risk was seen at 0400h (OR=5.7, Confidence interval = 5.6-5.8), with an OR of 11.4 (Ci=10.3-12.5) for fatal accidents at the same point. The same pattern was exhibited by single vehicle, head-on, and "other" (e.g., turning off the road) accidents, whereas overtaking and rear-end accidents did not show clear 24 hour patterns. Retaining alcohol-related accidents approximately doubled the nighttime peak for total accidents. During the winter, the peak of total accidents occurred at 03:00h (OR=3.8, Ci=3.5-4.0), five hours before sunrise, whereas the summer peak occurred at 04:00h (OR=11.6, Ci=11.3-11.9), shortly after the early summer sunrise and with consistently higher nighttime risk than for winter driving. It was concluded that early morning driving is several times more dangerous than driving during the forenoon. Apart from alcohol the effect seems related to sleepiness, but not to darkness.