Possibilistic decision theory has been proposed twenty years ago and has had several extensions since then. Even though ap-pealing for its ability to handle qualitative decision problems, possibilisticdecision theory suffers from an important drawback. Qualitative possibilistic utility criteria compare acts through min and max operators, which leads to a drowning effect. To over-come this lack of decision power of the theory, several refinements have been proposed. Lexicographic refinements are particularly appealing since they allow to benefit from the Expected Utility background, while remaining qualitative. This article aims at extend-ing lexicographic refinements to sequential decision problems i.e., to possibilistic decision trees and possibilistic Markov decision processes, when the horizon is finite. We present two criteria that refine qualitative possibilistic utilities and provide dynamic programming algorithms for calculating lexicographically optimal policies
