The current negotiating framework for WTO negotiations on agriculture includes flexibilities for "sensitive" products to be chosen by the importer. Without knowing which products their partners are likely to select, WTO members cannot assess the implications of an agreement for their market access opportunities. In this paper, we begin by specifying a Grossman-Helpman type political-economy welfare function, and use this to determine which products are likely to be selected as sensitive products. Assuming these products are subjected to smaller reduction in protection, we find that allowing even 2 percent of tariff lines to be treated as sensitive can greatly reduce the impact of an agreement on market access. This problem is, in part, a consequence of using a percentage of tariff lines as the constraint on the use of sensitive products. If the constraint on the products to be classified as sensitive takes more directly into account the interests of the exporter - being specified, for example, as a share of imports - then the adverse impacts on market access opportunities can be greatly reduced.