Health incentive schemes aim to produce healthier behaviours in target populations. They may do so both by making incentivised options more salient and by making them less costly. Changes in costs only result in healthier behaviour if the individual rationally assesses the cost change and acts accordingly. Not all people do this well. Those who fail to respond rationally to incentives will typically include those who are least able to make prudent choices more generally. This group will typically include the least advantaged more generally, since disadvantage inhibits one's effective ability to choose well and since poor choices tend to cause or aggravate disadvantage. Therefore, within the target population, health benefits to the better off may come at the cost of aggravated inequity. This is one instance of a problem I name the Able Chooser Problem, previously emphasised by Richard Arneson in relation to coercive paternalism. I describe and discuss this problem by distinguishing between policy options and their effects on the choice situation of individuals. Both positive and negative incentives, as well as mandates that are less than perfectly effective, require some sort of rational deliberation and action and so face the Able Chooser Problem. In contrast, effective restriction of what options are physically available, as well as choice context design that makes some options more salient or appealing, does not demand rational agency. These considerations provide an equity-based argument for preferring smart design of our choice and living environment to incentives and mandates.