We often get reason to doubt the reliability of some of our own reasoning. The rational response to such evidence would seem to depend on how reliable one should estimate that reasoning to be. Independence principles constrain that reliability-assessment, to prevent question-begging reliance on the very reasoning being assessed. But this has consequences some find disturbing: can it be rational for an agent to bracket some of her reasons—which she may, after all, be assessing impeccably? So several arguments have been offered against the very idea of an Independence principle. This paper argues that looking closely at these arguments actually strengthens the case for Independence, and yields some guidance in meeting a formidable challenge for Independence-defenders: formulating the principle in an adequate way.