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 harmful excessive 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 found 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.