The 2004 tax reform in Poland introduced a broad-base low-rate "flat" tax for business income. For the highest income taxpayers, the marginal tax rate fell from 40% to 19% at the cost of giving up tax preferences (broadening the base). The reform provides an opportunity to exploit difference-in-difference strategies relying on differential benefits from the reform among otherwise similar individuals, such as due to characteristics of the spouse. Relying on a large panel of individual tax return data we find very large increases in reported incomes and moderate tax revenue implications. These responses are most likely operating through reduction in tax avoidance or participation in grey economy and suggest that when avoidance margin is responsive base-broadening combined with marginal tax rate reductions can be welfare improving. The paper highlights empirical issues involved in estimating responsiveness of taxable income and suggests that violation of exclusion restrictions and heterogeneous earnings dynamics are likely responsible for "sensitivity" of results claimed elsewhere in the literature.