We propose a dynamic carbon tax (DCT) that stabilises gasoline prices by adjusting inversely to crude oil prices. By virtue of reducing gasoline price uncertainty and thus promoting the purchase of more fuel efficient vehicles, the DCT is expected to be more effective in cutting CO2 emissions than an equivalent ordinary fixed-rate carbon tax. By virtue of preventing or limiting gasoline price spikes, the DCT is also expected to receive greater public support. The analysis is structured into three parts. First, we show how any policy that reduces uncertainty about future gasoline prices improves the expected utility of more fuel efficient vehicles relative to that of less efficient ones. Second, we show how the DCT could be designed to stabilise gasoline prices and thereby reduce gasoline price uncertainty. Third, we test whether gasoline price volatility, taken as a proxy for gasoline price uncertainty, negatively affects the fuel efficiency of light-duty vehicles bought by US households. Using micro-data from the 2017 National Household Transport Survey, we find a negative correlation as expected despite limited volatility of gasoline prices in the study period.