In situations of peer disagreement there are two kinds of factors that matter. These are the factors internal to the discussion, such as evidence exposed and arguments presented by both sides and there are also factors external to the discussion, also called “independent factors”. The external factors include mainly virtues and competences of the participants. There are two main theories about epistemic disagreement, “the steadfast view” and “the conciliationism”, and each of them stresses the importance of one group of these factors over the other. This paper is a defense of the greater epistemic significance of independent factors over internal factors. However, it is not a defense of the conciliationism which takes independent factors to be systematically the ultimate arbiter in situations of peer disagreement. The argument in the paper goes like this. Although the steadfast view receives strong intuitive support from two cases presented by Thomas Kelly: “Right and Wrong” and “Wrong and Wronger”, I argue that the view is undermined by Timothy Williamson’s recent “Very Improbable Knowing” argument. This argument shows that for some basic type of evidence E when S uses it in favor of p, it is very improbable that S knows that S knows that p. Therefore, in situations of peer disagreement, S is unjustified to push her evidence in support of her side. There are arguably some exceptions, e.g. when one claims to have knowledge based on a priori evidence and on holistic evidence, but these are not sufficient to save the day for the steadfast view. In contrast to that, the reflective knowledge of one’s first order competences and virtues (i.e. external factors) is not vulnerable by Williamson’s argument. One reason for that is because we know about independent factors on the basis of holistic evidence. I claim that our epistemic goal in the face of peer disagreement is to end up on the side that is non-accidentally closer to truth. In accordance with achieving this goal, it is safer to stick to independent factors in resolving peer disagreement situations than to follow one’s nose concerning first-order evidence disclosed by the opponents. This might seem a counterintuitive result, which makes it worthy of further discussion.