In the existing sociological literature, the notion of accountability is seen both as a tool of sense-making (intelligibility side of accountability) and as a way of maintaining larger social order (normativity side of accountability). This paper points to drastically different ways of treating an interactional violation, depending on the precise framework within which the accountabilities associated with the violation are interpreted. The normative side of accountability involves the idea of interactional inequality—that is, the notion that people are not equally held accountable for their interactional violations. I suggest that such inequalities are strengthened by the prevailing cultural ideals and ideologies of interaction according to which a competent participant can solve interactional problems as they emerge. Problems of interaction are therefore commonly let pass, and if addressed, likely to be interpreted within the framework of intelligibility. This means that the violators are likely to get away from being held accountable in the normative sense of the term. As a result, I argue, many interactional problems are commonly beyond effective intervention. In its focus on the intelligibility side of accountability CA has, not only trouble addressing interactional inequalities, but it may also inherently undermine the severity of the inequalities to be addressed. A more critical, socially and societally relevant CA would thus benefit from a more explicit engagement with the normative side of the notion.