This paper explores the optimal income tax treatment of couples. Each couple is modelled as a single agent supplying labor along two dimensions: primary-earner and secondary-earner labor supply. We consider fully general nonlinear income tax schedules which creates a multi-dimensional screening problem. We prove that, under regularity and separability assumptions for utility functions and for a wide class of social welfare functions, optimal tax schemes display negative jointness such that the tax rate on one person decreases in the earnings of the spouse. We also show that the tax on the secondary earner tends to zero asymptotically as the earnings of the primary earner becomes large. These results are valid both in models where secondary earners make only a binary labor supply choice (work or not work), and in models where both spouses make continuous labor supply decisions. In the latter case and in contrast to the multi-dimensional screening monopoly model, the optimal tax system is regular everywhere with no bunching for a wide set of parameters.