This essay highlights an alternative tradition of understanding value conflicts in early Confucian thought. In contrast to a prominent position among interpreters that argues for the resolvability or harmonization of conflicting values, I argue that some early Confucians conceptualized value conflicts as irresolvable. In other words, when meaningful aspects of a situation come into tension with each other and values are threatened to be either left unfulfilled or harmed, early Confucians put forth a variety of views. Some believed that all values could be tended to as long as one had the moral imagination of a sage, whereas others saw the world as a place where irreconcilable conflicts between values could occur for even the most profound people. Within this diversity, I take up a view about irresolvable value conflicts where the confrontation with a deep value conflict leaves behind a moral remainder that can mar even the character of a sage.