Living with paradox through irony

•On the basis of our analysis, we argue that contradictions are co-constructed with three different forms of irony: inversive, subversive, and dramatic.•This leads us to develop a more general model that helps explain how irony may be used and may move discussions from one phase to another.•Especially, we show how irony puts contradictions into context through management strategies called ‘connecting.’•Our analysis supplies a missing piece to our understanding of how organizational members deal with paradox and adds to research on irony in organizations.