This article presents an empirical estimation of the effect of fuel prices on vehicle kilometers traveled (VKT) using a panel dataset of 1560 Swiss households over the period 2018–2021. Elasticities are estimated for different segments of households, based on their socio-demographic and vehicle characteristics, as well as on their driving intensity. Our results, based on fixed-effect, instrumental variable, and quantile regression models, indicate relatively large price elasticities and reveal heterogeneity in price sensitivity. Single-member households appear significantly more responsive to price than multiple-member households. Travel-intensive households do respond to changes in gasoline price, while less intensive drivers do not exhibit statistically significant price elasticities. For household segments who do not react to price, tailored non-price measures would be a useful complement to fuel taxes in order to reduce distance traveled and/or avoid imposing too strong a financial burden.