The authors propose and test a new "polyhedral" choice-based conjoint analysis question-design method that adapts each respondent's choice sets on the basis of previous answers by that respondent. Polyhedral "interior-point" algorithms design questions that quickly reduce the sets of partworths that are consistent with the respondent’s choices. To identify domains in which individual adaptation is promising (and domains in which it is not), the authors evaluate the performance of polyhedral choice-based conjoint analysis methods with Monte Carlo experiments. They vary magnitude (response accuracy), respondent heterogeneity, estimation method, and question-design method in a 4 × 2<sup>3</sup> experiment. The estimation methods are hierarchical Bayes and analytic center. The latter is a new individual-level estimation procedure that is a by-product of polyhedral question design. The benchmarks for individual adaptation are random designs, orthogonal designs, and aggregate customization. The simulations suggest that polyhedral question design does well in many domains, particularly those in which heterogeneity and partworth magnitudes are relatively large. The authors test feasibility, test an important design criterion (choice balance), and obtain empirical data on convergence by describing an application to the design of executive education programs in which 354 Web-based respondents answered stated-choice tasks with four service profiles each.