The potential use of genetic tests in insurance has raised concerns about discrimination and individuals losing access to health care either because of refusals to test for treatable diseases, or because test-positives cannot afford premiums. Governments have so far largely sought to restrict the use of genetic information by insurance companies. To date the number of tests available with significant actuarial value is limited. However, this is likely to change, raising more clearly the question as to whether the social costs of adverse selection outweigh the social costs of individuals not accessing health care for fear of the consequences of test information being used in insurance markets. In this contribution we set out the policy context and model the potential trade-offs between the losses faced by insurers from adverse selection by insurees (which will increase premiums reducing consumer welfare) and the detrimental health effects that may result from persons refusing to undergo tests that could identify treatable health conditions. It argues that the optimal public policy on genetic testing should reflect overall societal benefit, taking account of these trade-offs. Based on our model, the factors that influence the outcome include: the size of and value attached to the health gains from treatment; deterrent effects of a disclosure requirement on testing for health reasons; incidence of the disease; propensity of test-positives to adverse select; policy value adverse selectors buy in a non-disclosure environment; and price elasticity of demand for insurance. Our illustrative model can be used as a benchmark for developing other scenarios or incorporating real data in order to address the impact of different policies on disclosure and requirement to test.