The reliability of the travel time on a route is widely regarded as one of the dominant factors affecting the route and departure time choices of travelers. There is still a lack of consensus on the quantitative measures that best reflect travel time reliability. This paper addresses this question from a traveler's point of view. It was concluded from a large stated preference-revealed preference route choice experiment that a measure of the asymmetry of a travel time distribution (λskew) was an important reliability measure. Put simply, people prefer a route that is usually fast but sometimes quite costly over a route that can have any travel time over a long range. In terms of reliability there is a discrepancy between user-optimal choices and system-optimal choices, because the recent literature reveals that skewed travel time distributions may yield much higher (collective) costs than symmetric distributions. Although the results indicate that the degree of skew in the travel time distribution of a route largely affects travel choices, it is strongly argued that there is no one best measure, because what can be regarded as “best” is contingent on the goal that must be reached. In line with this view, it was found in more detailed analyses that travel information and travel purpose influenced travelers’ route choices. Further research should focus on elaborating the contingency view and on working with more individual-based reliability measures for route choice situations.