Choice-based conjoint analysis (CBC) is used widely in marketing for product design, segmentation, and marketing strategy. We propose and test a new "polyhedral" question-design method that adapts each respondent's choice sets based on previous answers by that respondent. Individual adaptation appears promising because, as demonstrated in the aggregate customization literature, question design can be improved based on prior estimates of the respondent's partworths – information that is revealed by respondents' answers to prior questions. The otherwise impractical computational problems of individual CBC adaptation become feasible based on recent polyhedral "interior-point" algorithms, which provide the rapid solutions necessary for real-time computation. To identify domains where individual adaptation is promising (and domains where it is not), we evaluate the performance of polyhedral CBC methods with Monte Carlo experiments. We vary magnitude (response accuracy), respondent heterogeneity, estimation method, and question-design method in a 4x23 experiment. The estimation methods are Hierarchical-Bayes estimation (HB) and Analytic-Center estimation (AC). 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. In the comparison of estimation methods, HB is strong across all domains, but AC estimation shows promise when heterogeneity is high. We close by describing an empirical application to the design of executive education programs in which 354 web-based respondents answered stated-choice tasks with four service profiles each. The profiles varied on eight multi-level features. With the help of this study a major university is revising its executive education programs with new formats and a new focus.