Abstract The decline of certain core modals in English, including may and might, is a well-documented phenomenon (cf. Daugs 2017). It is less clear, however, whether this tendency will lead to the loss of these modals or whether other changes are also underway. I aim to address this issue by looking at the use of may and might in concessive clauses. I will first present the results of a corpus study (COHA) aimed at understanding the diachronic development of concessive may and might. The analysis reveals a significant increase of may and might in concessive contexts since the 1960s, especially in factual concessives with but. This new finding is important as it shows that, though decreasing in frequency, the two modals are developing new patterns of use. This raises the question whether the status of may and might as modal verbs is also changing. I argue that the two verbs are going through a process of post-modal (secondary) grammaticalisation and constructionalisation, and that the concessive meaning is linked to the more complex ‘subj {may/might} VP, but-clause’ construction. I also claim that, within the paradigm of concessive constructions, those with may and might are best viewed as hedged concessives that serve politeness purposes.