In a discrete choice experiment, each respondent typically chooses the best product or service sequentially from many groups or choice sets of alternatives which are characterized by a number of different attributes. Respondents can find it difficult to trade off prospective products or services when every attribute of the offering changes in each comparison. Especially in studies involving many attributes, respondents get overloaded by the complexity of the choice task. To overcome respondent fatigue, it makes sense to simplify the comparison by holding some of the attributes constant in every choice set. A study in the health care
literature where eleven attributes were allocated across three different experimental designs with only five attributes being varied motivates the approach we present. However, our algorithmic approach is more general,allowing for any number of attributes and a smaller number of fixed attributes.