Public support and political mobilization are two crucial factors for the adoption of ambitious climate policies in line with the international greenhouse gas reduction targets of the Paris Agreement. Despite their compound importance, they are mainly studied separately. Using a random forest machine-learning model, this article investigates the relative predictive power of key established explanations for public support and mobilization for climate policies. Predictive models may shape future research priorities and contribute to theoretical advancement by showing which predictors are the most and least important. The analysis is based on a pre-election conjoint survey experiment on the Swiss CO2 Act in 2021. Results indicate that beliefs (such as the perceived effectiveness of policies) and policy design preferences (such as for subsidies or tax-related policies) are the most important predictors while other established explanations, such as socio-demographics, issue salience (the relative importance of issues) or political variables (such as the party affiliation) have relatively weak predictive power. Thus, beliefs are an essential factor to consider in addition to explanations that emphasize issue salience and preferences driven by voters' cost-benefit considerations.