Ambitious climate policy needs a mix of instruments, from relatively soft and supportive pull measures to more intervening and demanding push measures. Given that the latter often receive relatively low public support, especially when targeting consumers’ everyday life, we need to know more about how to increase their acceptability. We argue that existing research has focused on factors that explain relatively stable differences in climate policy support between countries and groups of people, which does not help much in improving the acceptability of specific policy instruments in a given country and society. There has been less research, and then often single-case or single-factor studies, on acceptability factors that policymakers can directly influence. This working paper aims to inspire much more research on such factors by critically reflecting on the status quo of existing research and knowledge and by formulating research needs, questions, and methodological approaches with regard to four clusters of politically influenceable acceptability factors: policy design and packaging, different temporal aspects of policies (timing, sequencing, trial runs), participation and coalition building, as well as information and framing.