Nearly all of the literature on the ethical, legal, or social issues surrounding genetic tests has proceeded on the assumption that any particular test for a gene mutation yields information about only one disease condition. Even though the phenomenon of pleiotropy, where a single gene has multiple, apparently unrelated phenotypic effects, is widely recognized in genetics, it has not had much significance for genetic testing until recently. In this article, I examine a moral dilemma created by one sort of pleiotropic testing, APOE genotyping, which can yield information about the risk of two different conditions -- coronary heart disease and Alzheimer's disease. A physician administering APOE testing for the beneficial purpose of assessing the risk of heart disease may discover medically useless and socially harmful information about the patient's risk of Alzheimer's disease. I explore how much providers should disclose to patients about pleiotropic test results and whether patients are obligated to know as much about their genetic condition as possible.