The use of deliberative mini-publics (DMPs), such as citizens’ assemblies, is becoming more common in climate policy-making across many countries. The upsurge of these methods reflects an acknowledgement of the need to engage the publics in policy choices that significantly impact their lives. Many DMPs to date have focused on the general challenge of decarbonization, across a range of policy areas. In this article, we first situate DMPs within the wider field of public engagement methods. We then draw from deliberative democratic theory and practice to argue that the next step for climate DMPs is to focus them on specific climate policy challenges and to embed and routinize their use in existing policy-making institutions. We present a case study of the targeted use of a climate DMP, which we designed and ran in partnership with the UK Climate Change Committee, focused on home energy decarbonization. We use this case study to explore barriers and challenges to embedding such an approach in climate policy-making institutions. Finally, we suggest ways that such challenges can be overcome and identify a number of tensions that must be navigated as DMPs become embedded in climate policy-making.