Calls for civility feature prominently in public discourse, and the concept has received growing attention by political philosophers recently. But what does it mean to be civil? The existing literature distinguishes between two main understandings of civility: civility as politeness and civility as public-mindedness. The objective of this article is to show that these conceptions and the different normative claims associated with them can all fit together. We argue that civility and incivility should be disaggregated in order to uncover fruitful connections between different aspects of the concept. We introduce a distinction between two dimensions of civility as public-mindedness (moral and justificatory), as well as a new distinction between the means and ends of civility. We examine the complex connections between the different dimensions of (in)civility and show that the disaggregation of civility and incivility tells us what kind of (in)civility matters, as well as when and why.