In a dynamic (sequential) framework, departures from the independence axiom (IND) are reputed to induce violations of dynamic consistency (DC), which may in turn have undesirable normative consequences. This result thus questions the normative acceptability of non expected-utility (non-EU) models, which precisely relax IND. This paper pursues a twofold objective. The main one is to discuss the normative conclusion: usual arguments linking violations of DC to departures from IND are shown to be actually based on specific (but usually remaining implicit) (...) assumptions which may rightfully be released, so that it is actually possible for a non-EU maximizer to be dynamically consistent and thus avoid normative difficulties. The second objective is to introduce a kind of `reality principle' (through two other evaluation criteria) in order to mitigate the normative requirement when examining adequate moods for non-EU decision making. (shrink)