Lack of public support for ambitious climate policy has acted as a major barrier to decarbonising economies across the world. This is especially true for the policy measure traditionally advanced by economists, namely carbon pricing, yet much less so for alternative measure such as subsidy programmes, or occasionally even command-and-control instruments. Building on these insights, the current study reports the results of a stated-preference survey administered to a representative sample of Swiss residents regarding five classes of policy tools. It contributes to the existing literature by taking into account two novel dimensions relevant to climate policy design under a net-zero target: first, rather than measuring support for stand-alone measures, we focus on optimal combinations of instruments; second, we distinguish their implementation between three sectors (transport, buildings, industry) rather than assuming economy-wide applications. In the context of our experiment, we find evidence of differentiated preference structures across sectors and an inclination towards mixes rather than stand-alone measures to reach climate neutrality. Drivers of relative instrument preferences are investigated thanks to regression models on a sectoral basis and key contributors identified. In addition, hierarchical clustering yields a nomenclature of stylised instrument mixes.