We use counterfactual analysis techniques to evaluate the impact of a $2 minimum unit price (MUP) on the distribution of Australian (Victorian) household off-trade alcohol purchases. Our estimates suggest that a $2 MUP significantly reduces the purchases of at-risk households by up to −0.92 [90% CI: −1.55, −0.28] standard drinks at the highest quantiles and has substantially less effect on households purchasing at light and moderate levels. A $2 MUP may reduce the proportions of male and female shoppers purchasing at the public health threshold of more than two standard drinks per household member per day by −3.03 [90% CI: −4.83, −1.22] percentage points (relative variation: −17%); and −1.85 [90% CI: −2.60, −1.10] percentage points (relative variation:−22%), respectively. Implementing an MUP on alcohol thus promises significant positive impacts on public health. Copyright © 2016 John Wiley & Sons, Ltd.