Extant theories of intertemporal choice entangle two aspects of time preference: impatience and time inconsistency. Impatient people focus on present consumption without worrying too much about the future; they may spend freely and avoid exercise. An outsider might question their choices, but impatient people do not experience conflict over those choices. By contrast, people who are time-inconsistent intend to save and exercise, but they fail to do so when temptation is proximate. Such individuals are conflicted; their preferences today differ from their preferences tomorrow. I characterize the interaction between impatience and time inconsistency in three leading models of temporal discounting that go beyond the exponential model, which does not predict time inconsistency at any level of impatience. The quasi-hyperbolic model predicts that time inconsistency increases with patience, whereas the hyperbolic model makes the opposite prediction. The constant-sensitivity model predicts that time inconsistency peaks at a moderate level of impatience. The results of an experiment using real monetary consequences with delays of up to one year align most closely with the prediction of the constant-sensitivity model. This paper was accepted by Yuval Rottenstreich, judgment and decision making.