We propose and test new adaptive question design and estimation algorithms for partial-profile conjoint analysis. Polyhedral question design focuses questions to reduce a feasible set of parameters as rapidly as possible. Analytic center estimation uses a centrality criterion based on consistency with respondents' answers. Both algorithms run with no noticeable delay between questions. We evaluate the proposed methods relative to established benchmarks for question design (random selection, D-efficient designs, adaptive conjoint analysis) and estimation (hierarchical Bayes). Monte Carlo simulations vary respondent heterogeneity and response errors. For low numbers of questions, polyhedral question design does best (or is tied for best) for all tested domains. For high numbers of questions, efficient fixed designs do better in some domains. Analytic center estimation shows promise for high heterogeneity and for low response errors; hierarchical Bayes for low heterogeneity and high response errors. Other simulations evaluate hybrid methods, which include self-explicated data. A field test (330 respondents) compared methods on both internal validity (holdout tasks) and external validity (actual choice of a laptop bag worth approximately $100). The field test is consistent with the simulation results and offers strong support for polyhedral question design. In addition, marketplace sales were consistent with conjoint-analysis predictions.