The article describes a recent Swiss popular initiative, aiming to replace the current system of statutory health insurance run by 61 competing private insurers with a new system run by a single public insurer. Despite the rejection of the initiative by 62% of voters in late September 2014, the campaign and ballot results are interesting because they show the importance of (effective) public communication in shaping the outcome of a popular ballot. The relevance of the Swiss case goes beyond the peculiarities of its federalism and direct democracy and might be useful for other countries debating the pros and cons of national unitary health insurance systems versus models using multiple insurers. After this electoral ballot, the project to establish a public sickness fund in Switzerland seems definitely stopped, at least for the next decade. Insurers, who opposed the initiative, have effectively fed the "fear of change" of the population and have stressed the good outcomes of the Swiss healthcare system. However, the political pressure favoured by the popular initiative opened a "windows of opportunity" and led the federal Parliament to pass a stricter regulation of health insurers, improving in this way the current system.