Most attributes in transportation studies, such as the travel time and the travel cost of a travel mode or road alternative, have a clear rank order in their attribute levels. Therefore one option in a choice set of an experimental design can dominate the other alternatives in the set. This research finds Bayesian D-efficient designs for a specific setup in the transportation field. It is shown that with a proper choice of prior information which adequately incorporates the dominance of lower attribute levels, no choice sets with a dominant alternative will be included in the efficient designs.