ABSTRACT: One defense of the “steadfast” position in cases of peer disagreement appeals to the idea that it’s rational for you to remain deeply agnostic about relevant propositions concerning your peer’s judgment, that is, to assign no credence value at all to such propositions. Thus, according to this view, since you need not assign any value to the proposition that your peer’s judgment is likely to be correct, you need not conciliate, since you can remain deeply agnostic on the question of how the likelihood of your peer’s judgment bears on the likelihood of your own. This paper argues that the case for deep agnosticism as a response to peer disagreement fails. Deep agnosticism (as a general thesis) implies that it is sometimes permissible to withhold judgment about whether there is a non-zero chance of a proposition’s being true. However, in cases of disagreement where deep agnosticism is supposed to support the steadfast position, such withholding isn’t rational. This is because of constraints placed on rational credence by objective probability or chance, which ensure that rational credence adequately reflects strength of evidence.