Most online retailers and content providers offer feature-based filtering tools to facilitate product search by their customers. We propose a method that learns about a customer's preferences each time he/she selects a screening feature, and then customizes the screening menu and displays the filtered alternatives in suitable order. It also allows a retailer to create adaptive displays showing the best alternatives for a highlighted feature. The proposed method has an offline component that estimates the parameters of a latent-class screening model, and an online component that uses Bayes' theorem to dynamically predict the sequential filtering of alternatives. We describe estimation procedures and illustrate adaptive customization using data from a choice experiment for electronic tablets.