In this talk we use climate tipping points as case study to investigate conditions under which scientists may legitimately communicate deeply uncertain scientific claims to policy-makers and the public. We identify three distinct concerns: the question of appropriate evidential standards for policy purposes; the legitimacy of appealing to deeply uncertain knowledge in policy advice; the problem of how properly to communicate deeply uncertain knowledge. We propose recommendations for addressing each of them: Decisions concerning the appropriateness of evidential standards need to be made communally and transparently; when uncertain knowledge should be communicated ought to be dependent on the needs and vulnerabilities of stakeholders, influencing what kind of knowledge is policy relevant and what science-policy decision framework we should adopt; the framing is key when it comes to inherently and deeply uncertain knowledge and here recent story-line approaches can play an important role.