Road bends are known to cause traffic crashes, but the hypothesis in this study was that small geographical areas with many road bends have less, not more, road casualties than comparable areas with fewer bends. Data on road crashes involving fatal, serious and slight casualties in 571 wards in Eastern England were examined against four measures of average road curvature (mean angle per bend, cumulative angle per km, number of bends per km and ratio of road distance to straight distance) using regression analysis. Taking account of other risk factors, measures of average road curvature in wards were negatively associated with crash numbers, especially for fatal crashes. The strongest associations were with the cumulative angle turned per km. The results add to evidence suggesting that road casualty risk effects vary with geographical scale. Although individual road bends might be hazardous, frequent bends have a protective effect over a few kilometres of road.