Maher (Philos Sci 59:120–141, 1992b) advances an objection to dynamic Dutch-book arguments, partly inspired by the discussion in Levi (The Monist 70:193–211, 1987; in particular by Levi's case 2, p. 204). Informally, the objection is that the decision maker will 'see the Dutch book coming" and consequently refuse to bet, thus escaping the Dutch book. Maher makes this explicit by modeling the decision maker's choices as a sequential decision problem. On this basis he claims that there is a mistake in dynamic coherence arguments. There is really no formal mistake in classical dynamic coherence arguments, but the discussions in Maher and Levi do suggest interesting ways in which the definition of dynamic coherence might be strengthened. Such a strengthened 'sequentialized" notion of dynamic coherence is explored here. It so happens that even on the strengthened standards for a Dutch book, the classic dynamic coherence argument for conditioning still goes through.