Climate research has shown that global warming will have adverse impacts on human well-being and nature, and that mitigation and adaptation effects continue to fall short. To prevent climate change, push measures like carbon taxes need to be part of the policy mix. Nevertheless, public support for push measures seems to be lacking, a phenomenon that cannot completely be explained by climate scepticism or individual and contextual influences beyond direct policy control, such as trust in government and local vulnerabilities. However, the role of specific policy design choices on public support has only recently been picked up by empirical studies, let alone the heterogeneous effects these policy design choices can have on different social groups. By use of a large-scale survey experiment among voters in the Netherland, this study examines the impact of policy design features on public support for push measures aimed at mitigating climate change. We show there is substantial variation in support for push measures depending on the specific issue a policy focusses on, and the impact it has on individual costs. Furthermore, we find that policy designs can have substantial effects on public support, especially structuring taxation in a consumption based progressive way (PolluterPayPrinciple) and earmarking revenue towards attractive pull measures, but that these effects differ between different policies. In addition, we find heterogeneous effects based on ideology. Overall, we demonstrate that policy design matters for public acceptance of carbon taxes, and that design choices should be policy specific to convince specific groups of citizens.