This paper presents a morphosemantic analysis of exclusivity which allows a uniform semantics for all exclusive operators. It accounts for the similar behavior of exclusives like only, merely and just, and explains their differences with compositional morphosemantic restrictions present for each lexical item. It highlights some of the broader uses of just, focusing on 'unexplanatory' just, and explains how they can be viewed as exclusive uses if we allow for covert elements in the alternative set. The reason that just exhibits this wider range of uses compared to other English exclusives is that it contains fewer morphosemantic restrictions, and is thus free to operate in a variety of contexts. In particular, this analysis argues that just is able to quantify over alternatives containing covert elements, allowing for a much wider and more context-dependent range of possible alternative sets. This move requires modifying some tenets of alternative semantics, including the Focus Principle, as the focus sensitivity of operators like only is taken to be lexically specific, rather than a property of all exclusives. This paper provides a framework for exploring the variation among exclusives and argues that alternative semantics should be extended beyond focus alternatives to allow for covert quantification.