Genetic models were fitted to self-report data on frequency of alcohol consumption and average quantity consumed when drinking, from 3,810 adult Australian twin pairs. Frequency of consumption is determined both by an abstinence dimension, which is strongly influenced by shared environmental effects but not by genetic effects, and by an independent frequency dimension, which is influenced by genetic effects in both sexes and possibly by shared environmental affects in men. Quantity of alcohol consumed is likewise determined by an environmental abstinence dimension and by an independent and partly heritable quantity dimension. The best-fitting model allowed for two routes to abstinence: those who were not abstainers by virtue of their position on the abstinence dimension could nonetheless become abstainers by their position on the second, frequency (or quantity) dimension. Heritability estimates were 66% in women and 42-75% in men, for frequency; and 57% in women and 24-61% in men, for quantity.