The networks considered in this paper consist of ring roads and equiangle spirals rotating in both directions. Journey lengths and numbers of crossings of paths are found for a circular city with uniformly and independently distributed origins and destinations of trips. The 30° spiral-and-ring network gives an average journey length 18 per cent less than a 90°-grid and 5 per cent less than a ring-and-radial network for this city. The minimum number of crossings of paths is about 14 per cent less than would be obtained if drivers could travel in straight lines between origin and destination. This minimum is obtained with a 70° spiral-and-ring network.