Evidence is often taken to be “normative” for doxastic agents. What accounts for the normativity of evidence? According to the view that I'll call “evidential minimalism”, there is a close connection between strong evidence for the truth of p and a normative reason to believe p: evidence is either itself a normative reason for belief, or evidence gives rise to such a reason when certain other minimal conditions are met. In this paper, I argue against evidential minimalism. I will argue that there are cases where: (i) an individual S possesses strong evidence E for the truth of p at time t, (ii) all other minimal conditions for the normativity of E are met at t, (iii) S doesn't believe p at t, yet (iv) S isn't open to any form of criticism on account of (i)–(iii) at t. I will then formulate a plausible linking claim connecting openness to criticism and the existence of normative reasons for belief. The minimalist can either accept or reject this linking claim. I will argue that, either way, the minimalist view falters.