It is a common intuition that the antecedent of an indicative conditional should have something to do with its consequent, that they should be somehow connected. In fact, many conditionals sound unacceptable precisely because they seem to suggest a connection which is not there. Although the majority of semantic theories of conditionals treat this phenomenon as something pragmatic, for instance, something that is conversationally implicated, no one has offered a full-fledged pragmatic explanation of why missing-link, and, in particular, false-link conditionals strike us as odd. The aim of this paper is to explore the possibility that the link is an example of a conversational implicature. We discuss possible tests one can employ to identify conversational implicatures, and, ultimately, we show that the connection between a conditional’s antecedent and consequent fails them all.