To compare estimated effects of two policy alternatives, (i) a minimum unit price (MUP) for alcohol and (ii) specific (per-unit) taxation, upon current product prices, per capita spending (A$), and per capita consumption by income quintile, consumption quintile and product type. Estimation of baseline spending and consumption, and modelling policy-to-price and price-to-consumption effects of policy changes using scanner data from a panel of demographically representative Australian households that includes product-level details of their off-trade alcohol spending (n = 885; total observations = 12,505). Robustness checks include alternative price elasticities, tax rates, minimum price thresholds and tax pass-through rates. Current alcohol taxes and alternative taxation and pricing policies are not highly regressive. Any regressive effects are small and concentrated among heavy consumers. The lowest-income consumers currently spend a larger proportion of income (2.3%) on alcohol taxes than the highest-income consumers (0.3%), but the mean amount is small in magnitude [A$5.50 per week (95%CI: 5.18-5.88)]. Both a MUP and specific taxation will have some regressive effects, but the effects are limited, as they are greatest for the heaviest consumers, irrespective of income. Among the policy alternatives, a MUP is more effective in reducing consumption than specific taxation, especially for consumers in the lowest-income quintile: an estimated mean per capita reduction of 11.9 standard drinks per week (95%CI: 11.3-12.6). Policies that increase the cost of the cheapest alcohol can be effective in reducing alcohol consumption, without having highly regressive effects.