This article provides a new perspective on the information structure of an agent in a standard model of adverse selection. Before contracting takes place, the agent has the opportunity to gather (private) information on a relevant parameter that affects final payoffs. I allow for the possibility that the agent remains uninformed with some probability. The agent's optimal choice of information structure is derived, and it is shown that in the case of two states of nature, the possibility of remaining ignorant has a positive strategic value for the agent. Since a poor information structure generates strategic benefits, there will be no equilibrium in which the agent is perfectly informed even if additional information is costless at the margin.