<p>Robert Aumann influentially claimed that the completeness axiom in utility theory is neither descriptively accurate nor normatively compelling. Separately, it’s commonly accepted that dynamic consistency in individual decision-making is a demand of rationality. These assertions may conflict, however, even in mundane decision problems lacking any form of preference change. I characterise the most permissive preference-based choice rule which allows an agent with incomplete but transitive preferences to satisfy a strong form of dynamic consistency. The resulting behaviour is not generally rationalisable by a completed preference relation. I thereby present a challenge to—and conditions for—the simultaneous satisfaction of strong dynamic consistency and preservation of preferential gaps.</p>