Feminist criticism of health care and of bioethics has become increasingly rich and sophisticated in the last years of the twentieth century. Nonetheless, this body of work remains quite marginalized. I believe that there are (at least) two reasons for this. First, many people are still confused about feminism. Second, many people are unconvinced that significant sexism still exists and are therefore unreceptive to arguments that it should be remedied if there is no larger benefit. In this essay I argue for a thin, "core" conception of feminism that is easy to understand and difficult to reject. Core feminism would render debate within feminism more fruitful, clear the way for appropriate recognition of differences among women and their circumstances, provide intellectually compelling reasons for current non-feminists to adopt a feminist outlook, and facilitate mutually beneficial cooperation between feminism and other progressive social movements. This conception of feminism also makes it clear that feminism is part of a larger egalitarian moral and political agenda, and adopting it would help bioethics focus on the most urgent moral priorities. In addition, integrating core feminism into bioethics would open a gateway to the more speculative parts of feminist work where a wealth of creative thinking is occurring. Engaging with this feminist work would challenge and strengthen mainstream approaches: it should also motivate mainstream bioethicists to explore other currently marginalized parts of bioethics.