Koopmans provided a well-known preference axiomatization for discounted utility, the most widely used model for maximizing intertemporal choice. There were, however, some technical problems in his analysis. For example, there was an unforeseen implication of bounded utility. Some partial solutions have been advanced in various fields in the literature. The technical problems in koopmans’ analysis obscure the appeal of his intuitive axioms. This paper completely resolves koopmans’ technical problems. In particular, it obtains complete flexibility concerning the utility functions that can be used. This paper, thus, provides a clean and complete preference axiomatization of discounted utility, clarifying the appeal of koopmans’ intuitive axioms.