 There is a further issue with the Converse Dutch Book theorem, because there are books that can be made against agents who violate other probabilistic norms, such as Reflection, countable additivity and others (see sections 3, 4, and 5). Satisfaction of the basic axioms is no guarantee that one will not be open to a book due to violation of some other norm. A correct formulation of the theorem must accordingly restrict the form and number of the allowable bets. Kemeny and Lehman put restrictions on the allowable bets (for example their betting systems are restricted to a finite number of bets), and these seem to rule out such counterexamples. However, it remains to be shown that avoiding book with such a restricted set of bets suffices to justify adherence to the axioms. The problem here becomes especially pressing with the observation, discussed in the following section, that incoherent agents need not be generally vulnerable to a sure loss, and thus that both coherent and incoherent agents alike may be subject to some books and not others. What is needed in arguing for adherence to the probability axioms is the further claim that the bets which lead to sure losses and that are associated with incoherence pose a special problem, although this threatens the use that many proponents of the DBA have wanted to make of Dutch Book arguments in defending other norms.