One of the least plausible assumptions of orthodox rational choice theory is that all rational agents have complete preferences over all possible prospects. If there are incommensurate values, for instance, this assumption fails. But what decision rules should agents use if they have incomplete preferences? Prominent proposals for decision making under uncertainty with incomplete preferences are vulnerable to diachronic money-pumps: they permit manifestly irrational sequences of choice. In this paper, I discuss strategies that are history-dependent, such as status quo maintenance and the sunk cost fallacy, and argue that such strategies are attractive because they (i) avoid a broad range of money-pumps, and (ii) are likely to be advantageous in strategic environments.