This paper develops a conceptual framework to analyze the political forces affecting the income-tax threshold in a non-linear tax system. First, we study how reforms affecting marginal tax rates and the income-tax threshold can be politically feasible. Our main theoretical results show the relationship between the types of reforms affecting the income-tax threshold and the identity of the pivotal voter who makes them politically feasible. In particular, we prove that the individual with median income is not necessarily decisive. Second, we highlight a mechanism "décote" used by French politicians to effectively control the number of households with positive income tax liability and show how it interacts with reforms of the statutory tax rates.