Decision-makers frequently struggle to base their choices on an exhaustive evaluation of all options at stake. This is particularly so when the choice problem at hand is complex, because the available alternatives are hard (if not impossible) to compare. Rather than striving to choose the most valuable alternative, in such situations decision-makers often settle for the choice of an alternative which is not inferior to any other available alternative instead. In this paper, we extend two established models of boundedly rational choice, the categorize then choose heuristic and the rational shortlist method, to incorporate this kind of “indecisive” choice behavior. We study some properties of these extensions and provide full behavioral characterizations.