This paper presents the results of a postal questionnaire survey of just over 4600 male drivers aimed at exploring the relationship between accidents and daytime sleepiness. Drivers in this survey provided details of the accidents they had experienced in the last 3 years, and identified those factors they thought had contributed to their accidents. In addition to the normal demographic and exposure variables, drivers completed the Epworth scale measuring daytime sleepiness. Drivers also reported whether they had felt close to falling asleep whilst driving during the past 12 months and whether the car they drove most was privately or company owned. The analysis of this data has identified the characteristics of tiredness-related accidents. The probability of feeling close to falling asleep at the wheel has been related to demographic variables and the Epworth score using a logistic model. Drivers reported that ca 7% of accident involvements were associated with tiredness (ca 9-10% of accidents). The accident liability of the drivers has been evaluated using a multivariate statistical model; for some drivers, accident liability is shown to be sensitive to daytime sleepiness.