In this three-chapter dissertation, I address three puzzles that arise from (or seem to arise from) taking higher-order evidence seriously. Higher-order evidence is evidence not directly about first-order propositions, but about the epistemic status of one's first-order beliefs. Taking such evidence seriously would lead us to the so-called 'level-connecting principles.' Although these principles have long been accepted, it has recently been recognized that they lead us to several puzzles. In Chapter 1, I discuss 'the Fumerton's puzzle,' which says that certain level-connecting principles would imply that a sufficient condition of rationality is impossible. I offer a solution by constructing a 'template' condition that can both be sufficient for rationality and also respect the level-connecting principles. In Chapter 2, I discussed the 'unmarked-clock puzzle' presented by David Christensen. I argue against a solution offered by Adam Elga and I propose a new one by arguing that the level-connecting principle Christensen relies on must have an admissibility clause. In Chapter 3, I deal with the dogmatism puzzle, which says that one's knowledge seems to entitle us to ignore all new contrary evidence. This puzzle assumes the socalled 'Entitlement Principle,' which says that knowing that one's evidence is misleading entitles one to ignore it. I argue that this principle is false. Specifically, I explain why we shouldn't treat knowledge that certain evidence is misleading as a sort of higher-order evidence about the credential of one's first-order evidence.