Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles and asked to select the one they consider best. Choice sets with no dominating or dominated profiles are called Pareto optimal, and these Pareto optimal choice sets are provided to respondents. However, if choice sets have too many profiles, they may be difficult to implement. Therefore, we provide strategies for reducing the number of profiles in choice sets. We consider situations where only a subset of interactions is of interest, and obtain connected main effects plans with smaller choice sets for 2^n and 3^n designs that are capable of estimating subsets of interactions inclusive of one specific factor. We also provide plans for estimating all main effects and one two-way interaction for mixed level designs. Next, we examine the relationship between certain Pareto Optimal choice sets and g-designs. Finally, we obtain connected main effects plans with smaller choice sets for estimating different subsets of interactions, not inclusive of one specific factor. / Statistics