Boghossian's discrimination argument for the incompatibility of externalism and a priori self-knowledge presupposes the relevant-alternatives account of knowledge, more precisely, the claim that the ability to rule out relevant alternatives is a necessary condition for knowledge. In the first two sections of this essay, I object to Boghossian's argument by showing that the standard way of supporting the claim just mentioned, namely with recourse to Goldman's famous barn example, will not convince a rational externalist who knows the relevant facts. In section three, a second challenge to the discrimination argument is developed. First, a descriptive variant of Goldman's barn example is distinguished from a demonstrative variant of this scenario. Then, it is argued that the fact that Goldman's protagonist does not have knowledge in the demonstrative variant cannot be explained by the claim that the ability to rule out relevant alternatives is necessary for knowledge. From this it is concluded that it is not possible to substantiate the claim just mentioned with recourse to Goldman's barn example. The upshot of the discussion in sections one through three is that one cannot argue for the incompatibility of externalism and a priori self-knowledge by drawing on the claim that the ability to rule out relevant alternatives is required for knowledge. In the final section of the article, it is shown that one can furthermore not argue for the incompatibility thesis by invoking the contention that so-called global reliability is necessary for knowledge.