Economists have an instinctively negative reaction to any government program that creates a "notch," that is, a discontinuity in a budget constraint. For example, welfare programs like public housing are structured so that a finite lump of benefits is lost all at once when a household's income crosses a certain threshhold. Such notches deserve their bad reputation --they effectively impose a high marginal tax rate over a small income range, which no doubt discourages work and promotes welfare dependency. However,this paper argues that in other contexts, tax and subsidy plans with notches should at least be considered as serious contenders when public policy seeks to encourage or discourage some activity. Using simulations,we show how notch schemes can dominate traditional linear schemes using a standard efficiency criterion.