There are increasing calls for the regulation of hedge funds, both for consumer protection and systemic reasons. We argue that the consumer protection arguments for direct regulation are not convincing, but find that the systemic concerns are sufficiently serious to warrant some forms of regulation. Existing regulatory methods, disclosure and activity restrictions, are unsuitable for hedge funds. Any future regulation must reduce the likelihood and potential costs of the failure of systemically important hedge funds whilst at the same time preserving the wider market benefits of hedge funds' ongoing activities.