This paper presents the properties of optimal piecewise linear income tax systems for families based on joint and individual incomes respectively. It models the interaction between the wage rates of mothers as "second earners" and variation in child care prices and productivities as determinants of across-household heterogeneity in second earner labour supply. We find that individual taxation welfare dominates joint taxation not only on the well-known grounds of efficiency but also of equity. An important driver of this result is the sharp rise in wage rates in the top percentiles of the primary wage distribution. In addition to reducing the intra-household net-of-tax wage gap, individual taxation removes the opportunity for tax avoidance income splitting makes available to high wage primary earners, leading to a much fairer distribution of the tax burden.