Restricting purchases or establishing a minimum (floor) price for low-cost, high-strength alcoholic beverages is an increasingly popular policy used to address problem drinking and alcohol-related harm. We study the consumption and short-term health-at-birth impacts of the 2006 Alice Springs Liquor Supply Plan (LSP) which effectively doubled the minimum per-unit price of alcohol by prohibiting sales of large containers of wine. Net alcohol consumption per person dropped by 12%. Both price and consumption remained unaffected in control regions. We estimated a price elasticity of demand for the cheapest drink in the market as low as -0.2. While this change decreased the total volume of pure alcohol consumed, it did not achieve a key policy objective to improve infant health outcomes among babies most at-risk for alcohol-related harm. We discuss mechanisms and potential policy conclusions.