<p>This paper addresses the issue of whether tax revenue from alcohol lost through cross-border shopping could be recouped by cutting excise duties. This in turn depends on the elasticity of demand for alcohol. We use data from the Family Expenditure Survey 1978-96 to estimate own- and cross-price elasticities of demand for beer, wine and spirits before and after completion of the Single Market. We find no evidence of a significant change in elasticities after the Single Market. The tax rates on beer and wine are currently below their revenue-maximising rates, implying that a cut in the duty rate on beer or wine would lead to a decrease in indirect tax revenue from alcohol. We cannot reject that the current tax rate on spirits is at the revenue-maximising rate, implying that further increases in the duty on spirits are likely to cause indirect tax revenue to fall. </p>