According to the classical Doctrine of Double Effect (DDE), there is a morally significant difference between intending harm and merely foreseeing harm. Versions of DDE have been defended in a variety of creative ways, but there is one difficulty, the so-called “closeness problem”, that continues to bedevil all of them. The problem is that an agent's intention can always be identified in such a fine-grained way as to eliminate an intention to harm from almost any situation, including those that have been taken to be paradigmatic instances in which DDE applies to intended harm. In this paper, we consider and reject a number of recent attempts to solve the closeness problem. We argue that the failure of these proposals strongly suggests that the closeness problem is intractable, and that the distinction between intending harm and merely foreseeing harm is not morally significant. Further, we argue that there may be a deeper reason why such attempts must fail: the rationale that makes the best fit with DDE, namely, an imperative not to aim at evil, is itself irredeemably flawed. While we believe that these observations should lead us to abandon further attempts to solve the closeness problem for DDE, we also conclude by showing how a related principle that is supported by a distinct rationale and avoids facing the closeness problem altogether nevertheless shares with DDE its most important features, including an intuitive explanation of a number of cases and a commitment to the relevance of intentions.