Possibilistic decision theory has been proposed twenty years ago and has had several extensions since then. Because of the lack of decision power of possibilistic decision theory, several refinements have then been proposed. Unfortunately, these refinements do not allow to circumvent the difficulty when the decision problem is sequential. In this article, we propose to extend lexicographic refinements to possibilistic decision trees. We show, in particular, that they still benefit from an Expected Utility (EU) grounding. We also provide qualitative dynamic programming algorithms to compute lexicographic optimal strategies. The paper is completed with an experimental study that shows the feasibility and the interest of the approach.