This paper discusses two conservative ways of treating evidence. (I) Closing inquiry involves discounting evidence bearing on one's belief unless it is particularly strong evidence; (II) biased assimilation involves dedicating more investigative resources to scrutinizing disconfirming evidence (than confirming evidence), thereby increasing the chances of finding reasons to dismiss it. It is natural to worry that these practices lead to irrational biases in favor of one's existing beliefs, and that they make one's epistemic condition significantly path-sensitive by giving a bigger role to batches of evidence obtained earlier in the course of inquiry compared with those subsequently acquired. However, I argue that both practices are demanded by considerations of practical rationality. I also argue that, contrary to initial appearances, there is little reason to worry about the effects of these practices on the dynamics of one's beliefs.