We study the link between tax progressivity and top income shares. Using variation from large-scale Western tax reforms in the 1980s and 1990s and the novel synthetic control method, we find large and lasting boosting impacts on top income shares from the progressivity reductions. Effects are largest in the very top groups while earners in the bottom half of the top decile were almost unaffected by the reforms. Cuts in top marginal tax rates account for most of this outcome whereas reduced overall progressivity contributed less. Searching for mechanisms, real income responses as measured by growth in aggregate GDP per capita, registered patents and tax revenues were unaffected by the reforms. By contrast, tax avoidance behavior related to the management of capital incomes in the very income top appears to lie behind the observed effects.