Using unique data on Swedish households, we measure the price elas- ticity of electricity demand for households facing a mandatory non-linear distribution tariffs where households are charged based on their maximum consumption during a month, and where the marginal incentives are very large. We estimate the price elasticity using both 2SLS and bunching esti- mators, and we find that the price elasticity is smaller than what previous literature on electricity demand have found. Furthermore, we illustrate why charging households based on maxi- mum consumption during a month leads to weak incentives in the end of the month, and discuss alternative tariff designs.