<p>In<i> Epistemic Explanations</i>, Ernest Sosa invokes a classical normative threshold account of rational judgment and suspension, according to which it is rational to judge that P iff one has a sufficiently high credence in P, and rational to suspend judgment about P iff one has a middling credence in P. I argue that threshold views of this kind face serious problems traceable to their foundation in classical probability theory. Moreover, I argue, the difficulty of bridging the gap between traditional and gradable (or quantitative) doxastic attitudes should prompt classical threshold theorists to reframe their analysis of traditional doxastic attitudes in terms of gradable ones freed from the constraints of classical probability theory. I develop such a non-classical threshold view, modeled on the Dempster–Shafer theory of evidence. Because this framework relies on non-additive probabilities, how high one’s credence is in P is irrelevant to whether it is rational to judge that P (or not-P) or suspend on P. On the alternative threshold view I propose, whether it is rational to judge or suspend depends instead on the absolute distance between one's probability distribution over P and not-P. This non-classical alternative, I argue, avoids the tensions that beset classical threshold views.</p>