About a decade ago, Adam Elga introduced philosophers to an intriguing puzzle. In it, Sleeping Beauty, a perfectly rational agent, undergoes an experiment in which she becomes ignorant of what time it is. This situation is puzzling for two reasons: First, because there are two equally plausible views about how she will change her degree of belief given her situation and, second, because the traditional rules for updating degrees of belief don’t seem to apply to this case. In this dissertation, my goals are to settle the debate concerning this puzzle and to offer a new rule for updating some types of degrees of belief. Regarding the puzzle, I will defend a view called “the Lesser view,” a view largely favorable to the Thirders’ position in the traditional debate on the puzzle. Regarding the general rule for updating, I will present and defend a rule called “Shifted Jeffrey Conditionalization.” My discussions of the above view and rule will complement each other: On the one hand, I defend the Lesser view by making use of Shifted Jeffrey Conditionalization. On the other hand, I test Shifted Jeffrey Conditionalization by applying it to various credal transitions in the Sleeping Beauty problem and revise that rule in accordance with the results of the test application. In the end, I will present and defend an updating rule called “General Shifted Jeffrey Conditionalization,” which I suspect is the general rule for updating one’s degrees of belief in so-called tensed propositions.