Questions about information inform many debates in bioethics. One of the reasons for this is that at least some level of information is taken by many to be a prerequisite of valid consent. For others, autonomy in the widest sense presupposes information, because one cannot be in control of one's life without at least some insight into what it could turn out to contain. Yet not everyone shares this view, and there is a debate about whether or not there is a right to remain in ignorance of one's medical, and especially genetic, information. It is notable, though, that this debate leaves unexamined the assumption that, if a person wants information, he is entitled to it. This paper examines the assumption, specifically in relation to genetics, where learning facts about oneself may reveal facts about other people, particularly one's close relatives. This may be taken as a violation of their privacy, and since privacy is something that we normally think should be respected, it is worth asking whether one ought to abjure the opportunity to obtain genetic information for the sake of privacy. In effect, there may be an argument to be made not just for a right to remain in ignorance, but for a duty to do so.