This article forms a contribution to the ongoing scholarly debate on the possible effect of jus cogens norms. For the purpose of the article, it is assumed that peremptory norms certainly exist in positive international law. According to the argument, even if we limit the effects of jus cogens norms to those described in the 1969 Vienna Convention, the jus cogens concept takes us farther than most commentators seem to realize. This is due partly to the power potential invested in the jus cogens concept, partly to the intricate structure typical of legal norms. In fact, as argued in this article, if we take the existence of peremptory international law to its logical consequence, it will carry too far: most actors on the international arena will consider the effects unacceptable. Using as an example the jus cogens norm most often referred to in the literature – the principle of non-use of force – it is a purpose of the present article to establish this proposition as valid. A second purpose is to attract attention to what appears to be the really crucial question for further discussion: How should the effects of jus cogens be limited? Whoever opened the Pandora's Box that once contained the jus cogens concept obviously did not fully realize the consequences that this would have for international law in general. How can this situation be remedied?