Rescorla (2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R.A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identiﬁed(Briggs &Pettigrew,2018). In both cases, these arguments proceed by ﬁrst establishing a very general reﬂection principle.