Religious wars in Switzerland

The Wars of Religion bloodied Europe in the 16th and 17th centuries. These conflicts, and the famines that ensued, resulted in several million deaths. During the same period, the former Swiss Confederation experienced four wars of religion. The two Kappel Wars in 1529 and 1531, and the two Villmergen Wars in 1656 and 1712, claimed around 2,000 lives. How is it that the cantons, themselves divided between Reformed and Catholics, were not drawn into these European religious wars?