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In this article, we introduce a novel approach to computing the fewest-turn map directions or routes based on the concept of natural roads. Natural roads are joined road segments that perceptually constitute good continuity. This approach relies on the connectivity of natural roads rather than that of road segments for computing routes or map directions. Because of this, the derived routes possess the fewest turns. However, what we intend to achieve are the routes that not only possess the fewest turns but are also as short as possible. This kind of map direction is more effective and favored by people because they bear less cognitive burden. Furthermore, the computation of the routes is more efficient because it is based on the graph encoding the connectivity of roads, which is substantially smaller than the graph of road segments. We experimented on eight urban street networks from North America and Europe to illustrate the above-stated advantages. The experimental results indicate that the fewest-turn routes possess fewer turns and shorter distances than the simplest paths and the routes provided by Google Maps. For example, the fewest-turn-and-shortest routes are on average 15% shorter than the routes suggested by Google Maps, whereas the number of turns is just half as much. This approach is a key technology behind FromToMap.org - a web mapping service using openstreetmap data. [ABSTRACT FROM AUTHOR]