The paper addresses a popular argument that accounts of assertion in terms of constitutive norms are incompatible with conventionalism about assertion. The argument appeals to an alleged modal asymmetry: constitutive rules are essential to the acts they characterize, and therefore the obligations they impose necessarily apply to every instance; conventions are arbitrary, and thus can only contingently regulate the practices they establish. The paper argues that this line of reasoning fails to establish any modal asymmetry, by invoking the distinction between (...) the non-discriminating existence across possible worlds of types of practices and institutions defined by constitutive rules, and the discriminating existence of those among them that are actually in force, and hence truly normative. The necessity of practices defined by constitutive rules that the argument relies on concerns the former, while conventionalist claims are only about the latter. The paper should thus contribute to get a better understanding of what social constructs conceived as defined by constitutive norms are. It concludes by suggesting considerations that are relevant to deciding whether assertion is in fact conventional. (shrink)