Two important tasks for theorists of justice are to determine the bounds of justice, which explain why some claims are matters of justice and others are not, and to determine the demands of justice, which settle conflicts that fall within those bounds. In this paper, we clarify the distinction between bounds and demands, revealing two striking things. First, while thresholds have typically been understood to be demands of justice, their use as such is confusing and arguably implausible. Second, thresholds appear to be better understood as demarcating the bounds of justice, if a suitable explanation for their use can be found. We explore three explanations for why thresholds can demarcate bounds and assess the prospects for seeing thresholds in this new and different role. These are satiability of the value of goods, satiability of justice, and conceptual engineering.