Consider a horizontal curve set between two tangents forming a given deflection angle. Choosing a larger degree of curve (shorter radius) will make the tangents longer and the curve shorter and sharper. The question examined here is how this simultaneous change of several geometric elements affects the overall accident frequency. After a review of the relevant literature it is shown that increasing the degree of curve always increases the expected accident frequency. Also a simple way to compute the approximate amount of accident increase is described. It can be shown that the choice of degree of curve has large safety consequences when the deflection angle is large. This is not currently reflected in geometric design standards. It can also be shown that, contrary to commonly held opinion, adding x meters to the radius has the same effect on accident frequency regardless of whether the radius is 100 m or 1000 m. Finally, the effect of tangent length on curve accidents is added to the mix and a computational scheme to aid the selection of the degree of curve in specified circumstances of tangent lengths and deflection angle is provided.