The question of whether two drugs - namely alcohol and tobacco - are used as complements or substitutes is of crucial interest if side-effects of anti-smoking policies are considered. Numerous papers have empirically addressed this issue by estimating demand systems for alcohol and tobacco and subsequently calculating cross-price effects. However, this traditional approach often is seriously hampered by insufficient price-variation observed in survey data. We therefore suggest an alternative instrumental variables approach that statistically mimics an experimental study and does not rely on prices as explanatory variables. This approach is applied to German survey data. Our estimation results suggest that a reduction in tobacco consumption results in a moderate reduction in alcohol consumption. It is shown theoretically that this implies that alcohol and tobacco are complements. Hence, we conclude that successful anti-smoking policies will not result in the unintended side-effect of an increased (ab)use of alcohol.