Why think that our doxastic states should obey norms of formal coherence? One sort of answer to this question attempts to justify coherence in instrumental terms, arguing that only by being coherent can we achieve some more fundamental goal, such as true belief. Here I consider apparent counterexamples to this instrumental strategy: cases in which being incoherent seems like the best way of achieving epistemic goals. Although the cases differ considerably in their surface structure, I provide a common diagnosis, claiming that the cases implicitly depend on contentious assumptions about the range of possible states that count as relevant alternatives to be considered in pursuing our epistemic goals. I suggest that, by substituting a range of such states that is independently better motivated, we may preserve the viability of the instrumental strategy.