According to an increasingly popular view known as non-doxasticism, religious faith need not include belief, but only some cognitively weaker attitude. This view comes with great promises, as it offers a way for the agnostic to partake in religion. My concern is how such a non-doxastic faith might be understood as a rational attitude. I offer three desiderata for any account of rational, non-doxastic faith. These desiderata are based on general considerations regarding epistemic rationality, and on major themes from current literature on the closely related notions of trust and hope. The first desideratum states that faith must be able to meet the demands of reason. The second requires, perhaps surprisingly, that faith should not imply trust. The third requires that faith should imply hope while excluding despair. I show how several prominent accounts of non-doxastic faith, by Lara Buchak, Daniel Howard-Snyder and Daniel McKaughan, all fail to meet at least one of these desiderata. I also suggest that the desiderata should make us prefer a reconstructive methodology.