Income shifting arises as one of the key questions when thinking about the design of a tax system as a whole. We study a simple economy, involving a benevolent policy-maker and a population of agents differing in terms of productivities, labor supply elasticities, and shifting costs. Paying special attention to the cost structure of income shifting, we highlight that when people who shift easily along the extensive margin are also more elastic in labor supply, giving them a lower tax rate is a good thing, and the government should not necessarily combat income shifting. This mechanism may be compared to third-degree price discrimination in industrial organization and works as a form of endogenous tagging. We explore this possibility numerically before showing that our results derived for a policy-maker optimally adjusting two linear tax instruments carry over when two fully non-linear taxes are potentially available.