Almost all regulatory policy stops at the national border. Thus, when conducting business abroad, the behaviour of firms i s r egulated b y t heir h ost, n ot t heir home country. Yet, international institutions have issued (non-binding) codes of conduct on social/environmental aspects of firm behaviour, and various high-income countries discuss how to improve extraterritorial firm b ehaviour -w ith h igh p olitical contestation over the appropriate mix of state intervention and corporate self-regulation. Exploiting a unique national referendum on this issue in Switzerland, we investigate how these interact from a public opinion standpoint. Based on a nationally representative survey experiment (N=1564), we find that while baseline support for state intervention is high (approx. 60%), corporate self-regulation decreases such support. However, only credible voluntary business initiatives lead to substantial reductions. Our results speak to a broad policy debate in European countries and the EU on how to ensure compliance of firms with human rights and environmental standards.