Recent studies with Spanish data suggest that indirect taxation is a potential instrument to reduce tobacco consumption but the magnitude of the estimated price elasticity limits the effectiveness of the taxes. However, if the separability restriction does not hold between tobacco and other goods, the results obtained could be misleading. This shortcoming of previous analyses leads us to formulate a demand system with alcohol, tobacco and other goods so as to estimate and test complementary effects and to assess the possibility for reducing consumption by indirect taxation of complementary commodities. We use the Spanish Family Expenditure Survey to carry out a cross-section study which allows us to estimate demand models under different assumptions about the nature of zero expenditures and to test the effectiveness of indirect taxation. The findings tend to support our initial suspicions about the inadequacy of imposing separability and point out the importance of alcohol taxation to reduce tobacco consumption. However, given the structure of the data used, these results should be viewed with caution and must be confirmed by additional evidence.