The relationship between various measures of traffic speed, under free flow conditions, and accident rate is investigated for two groups of sites, one in the Tyne and Wear county of the UK and the other in Bahrain. The effect of speed limits on traffic speed is estimated for both groups of sites. In Bahrain, there is statistically significant evidence of an association between mean speed and accident rate. In Tyne and Wear the statistical evidence is weaker, and points to a stronger relationship between accidents and the variability of traffic speeds. In both areas, there is an apparent decrease in accident rate if the percentage of heavy vehicles increases, with the speed distribution held constant. In both areas the effect of speed limits is to reduce the mean speed of traffic by at least one quarter. Higher speeds are associated with longer trips.