Volume discounts encourage consumers to buy more. Banning such discounts should then lead to consumers buying less. This is the thinking behind banning multiple-unit discounts, including multibuy price promotions, to curb excessive harmful consumption of alcohol and high-fat, -sugar, and -salt (HFSS) foods. However, our analysis questions the validity of this thinking, which ignores the possible restraining effect of volume discounts. We find that such a ban for retailing alcohol in Scotland increased rather than reduced sales. Retailers switched to using more straight (single-unit) discounts, which encouraged high-consumption households to increase their shopping frequency and buy more.