Acceptability is a thoroughly normative epistemic notion. If a statement is acceptable, i.e. it is proper to take it as a premise, then one is justified in accepting it. We also hold that a statement is acceptable just in case there is a presumption of warrant in its favor. We thus see acceptability connected to epistemic normativity on the one hand and to warrant on the other. But there is a distinct tension in this dual connection. The dominant tradition in modern epistemology sees epistemic justification as an internalist notion. We are justified in holding a belief just in case certain conditions are fulfilled of which we have privileged access. Warrant is an externalist notion. We have no privileged access to the conditions of warrant. Is our understanding of acceptability as both normative and definable in terms of presumption of warrant philosophically coherent? We shall argue that it is a philosophically coherent notion. Presumption of warrant, unlike warrant, is an internalist notion. Our position can be characterized as an externalist internal ism. It avoids the charge brought against externalism of allowing one to be justified in accepting some claim even if one has no evidence for it. We meet the classical internalist challenge that acceptance is normatively proper only if one has done one's epistemic duty and thus one is aware of the normative propriety of the acceptance by providing a non-deontological definition of epistemic justification, and arguing that this is still a sufficiently normative notion for acceptability.