This paper presents the properties of optimal piecewise linear income tax systems for families, based on joint and individual incomes. It models the interaction between the wage rates of mothers as "second earners" and variation in child care prices and productivities as determinants of heterogeneity in second earner labour supply. We find that individual taxation welfare dominates joint taxation on grounds of both efficiency and equity. Heterogeneous labour supplies, the positive relationship between household wages and child care quality, and the sharp rise in wage rates in the top percentiles of the primary wage distribution account for this result. In addition to reducing the intra-household net-of-tax wage gap, individual taxation removes the opportunity for tax avoidance that income-splitting makes available to high-wage primary earners, leading to a much fairer distribution of the tax burden.