Non-expected utility theories, such as rank dependent utility (RDU) theory, have been proposed as alternative models to EU theory in decision making under risk. These models do not share the separability property of expected utility theory. This implies that, in a decision tree, if the reduction of compound lotteries assumption is made (so that preferences at each decision node reduce to RDU preferences among lotteries) and that preferences at different decision nodes are identical (same utility function and same weighting function), then the preferences are not dynamically consistent; in particular, the sophisticated strategy, i.e., the strategy generated by a standard rolling back of the decision tree, is likely to be dominated w.r.t. stochastic dominance. Dynamic consistency of choices remains feasible, and the decision maker can avoid dominated choices, by adopting a non-consequentialist behavior, with his choices in a subtree possibly depending on what happens in the rest of the tree. We propose a procedure which: (i) although adopting a non-consequentialist behavior, involves a form of rolling back of the decision tree; (ii) selects a non-dominated strategy that realizes a compromise between the decision maker’s discordant goals at the different decision nodes. Relative to the computations involved in the standard expected utility evaluation of a decision problem, the main computational increase is due to the identification of non-dominated strategies by linear programming. A simulation, using the rank dependent utility criterion, confirms the computational tractability of the model.