Rational credence should be coherent in the sense that your attitudes should not leave you open to a sure loss. Rational credence should be such that you can learn when confronted with relevant evidence. Rational credence should not be sensitive to irrelevant changes in epistemic situation. While all plausible, these three desiderata are in conflict in a deep way. This paper explores some aspects of the tension through a study of the problem of belief inertia for imprecise probabilities.