There is a basic tension between the principle of democracy and the rule of law. This becomes obvious whenever the Swiss citizens accept an initiative that is incompatible with the European Convention on Human Rights. First, we discuss the traditions behind these two principles before we survey the empirical papers about the relation between direct democracy and minority rights in the US as well as in Switzerland. Then we discuss the literature on the relation between direct democracy and death penalty. There, the conflict becomes rather obvious. Solutions, which will always involve compromises between these two principles, necessitate some  role  of  the  Supreme  Court,  at  the  cost  of  some,  but  only  minor  limitations  of  direct popular rights.