As universal health coverage becomes the norm in many countries, it is important to determine public priorities regarding benefits to include in health insurance coverage. We report results of participation in a decision exercise among residents of Switzerland, a high-income country with a long history of universal health insurance and deliberative democracy. We adapted the Choosing Healthplans All Together (CHAT) tool, an exercise developed to transform complex healthcare allocation decisions into easily understandable choices, for use in Switzerland. We conducted CHAT exercises in twelve Swiss cities with recruitment from a range of socio-economic backgrounds, taking into account differences in language and culture. Compared to existing coverage, a majority of 175 participants accepted greater general practice gatekeeping (94%), exclusion of invasive life-sustaining measures in dying patients (80%), longer waiting times for non-urgent episodic care (78%), greater adherence to cost-effectiveness guidelines in chronic care (66%), and lower premium subsidies (51%). Most initially chose greater coverage for dental care (59%), quality of life (57%), and long-term care (90%). During group deliberations, participants increased coverage for out-of-pocket costs (58%) and mental health to current levels (41%) and beyond current levels for rehabilitation (50%), and decreased coverage for quality of life to current levels (74%). Following group deliberation, they tended to change their views back to below current coverage for help with out-of-pocket costs, and back to current levels for rehabilitation. Most participants accepted the plan as appropriate and fair. A significant number would have added nothing. Swiss participants who have engaged in a priority setting exercise accept complex resource allocation trade-offs in healthcare coverage. Moreover, in the context of a well-funded healthcare system with universal coverage centered on individual choice, at least some of our participants believed a fully sufficient threshold of health insurance coverage was achieved.