Scholars and practitioners discuss how to increase the policy impact of climate assemblies (CAs) noting that their proposals tend to be more ambitious than government policy. CAs comprise groups of randomly selected citizens (minipublics) who deliberate on climate policy issues. We argue for greater focus on how political actors strategically use CAs and suggest welcoming some of this strategic use. We propose that CAs, and minipublics more generally, need political embedding. That means, minipublic designers should first consider how political actors will likely interact with a process given their interests and political context, and subsequently make deliberate use of strategies to foster objectives like policy impact. Using a thought experiment, we then demonstrate that the effectiveness of such political embedding strategies to promote CAs’ policy impact depends on political context. Our analysis shows that the impacts of mass publicity, commissioning actors, inclusion of perspectives, and strategic framings vary with the constellation of interests of climate political actors. This exercise challenges sweeping statements about optimal CA and minipublic design, contributing to more realistic theorizing. Considering political embeddedness will help democratic reformers assess potential models for minipublic institutionalization more accurately.