We use a semi-parametric conditional median as a robust alternative to the parametric conditional mean to estimate the gasoline demand function. Our approach protects against data and specification errors, and may yield a more reliable basis for public-policy decisions that depend on accurate estimates of gasoline demand. As a comparison, we also estimated the parametric translog conditional mean model. Our semi-parametric estimates imply that gasoline demand becomes more price elastic, but also less income elastic, as incomes rise. In addition, we find that demand appears to become more price elastic as prices increase in real terms.