Horizontal curves are found on all roads. The relationship between the characteristics of horizontal curves and the number of accidents is complex and no previous study has included all factors that are potentially influential for accidents. This paper presents a study of 63 969 horizontal curves on rural two-lane roads in Norway. Accident prediction models including more characteristics of horizontal curves than used in any previous study were developed. Most of the characteristics were found to be related to the number of accidents. Most coefficients were consistent with those found in previous studies, but some findings were surprising. Compound curves, which are curves in which radius varies throughout the curve, were found to be safer than circular or nearly circular curves. A steeper slope of a vertical grade before a curve is associated with fewer accidents.