This paper derives optimal top tax rate formulas in a model where top earners respond to taxes through three channels: labor supply, tax avoidance, and compensation bargaining. The optimal top tax rate increases when there are zero-sum compensation-bargaining effects. We present empirical evidence consistent with bargaining effects. Top tax rate cuts are associated with top one percent pretax income shares increases but not higher economic growth. US CEO "pay for luck" is quantitatively more prevalent when top tax rates are low. International CEO pay levels are negatively correlated with top tax rates, even controlling for firms' characteristics and performance.