This paper studies the role of exchange policies as a price discrimination device in a sequential screening model with heterogeneous goods. In the first period, agents are uncertain about their ordinal preferences over a set of horizontally differentiated goods, but have private information about their intensity of preferences. In the second period, each individual privately learns his preferences and consumption takes place. Revenue maximizing mechanisms are completely characterized. They partially restrict the flexibility between the goods in the second stage for consumers that care little about which variety they obtain while granting always the favorite good to consumers that care much. The optimal design of the partial restriction of flexibility can be implemented by offering Limited Exchange Contracts. A Limited Exchange Contract consists of an initial product choice and a subset of products to which free exchange is possible in the second period. The use of exchange fees in contracts is not optimal for the purpose of price discrimination.