We estimate the rebound effect for motor vehicles, by which improved fuel efficiency causes additional travel, using a panel of US states for 1966-2001. Our model accounts for endogenous changes in fuel efficiency, distinguishes between autocorrelation and lagged effects, includes a measure of the stringency of fuel-economy standards, and interacts the rebound effect with income. At sample averages of variables, our 3SLS estimates of the short- and long-run rebound effect are 4.7% and 22.0%. But they decline substantially with income: with variables at 1997-2001 levels they become 2.6% and 12.1%, considerably smaller than typically assumed for policy analysis.