Vastly increased transnational business activity in recent decades has been accompanied by controversy over how to cope with its social and environmental impacts, particularly in the context of firms from high-income countries operating in less developed nations. The most prominent policy response thus far consists of new international soft law, e.g. the UN Guiding Principles on Business and Human Rights. It remains open, however, whether and how such soft law could bring about more responsible corporate behavior abroad. We submit that the most effective mechanism to this end may operate through stricter home-country regulation of corporate behavior abroad. Exploiting a unique national initiative on this subject in Switzerland, we use a choice experiment with a large representative sample of voters (N=3010) to study public demand for such regulation. Contrary to conventional wisdom emphasizing fear of sovereignty loss and/or economic disadvantages from unilateral regulation of transnational activity, our results show that citizens prefer very strict and unilateral rules, while correctly assessing their consequences. Mechanism tests with survey-experimental vignettes reveal that citizens are aware that such rules are economically costly, entailing competitive disadvantages, but would be more effective in tackling the problem, normatively appropriate and reputation enhancing for the home country. Moreover, exposure to information highlighting international norm-setting in this area leads to even stronger demand for stricter rules. These findings indicate surprisingly strong public support for making international soft law effective via enforceable domestic regulation, even if direct regulatory benefits accrue abroad while regulatory costs materialize at home. They also suggest that effective communication of international norms is one pathway through which international soft law can effectively change business behavior.