The ‘limits of markets’ debate broadly concerns the question of when it is (im)permissible to have a market in some good. Markets can be of tremendous benefit to society, but many have felt that certain goods should not be for sale (e.g., sex, kidneys, bombs). Their sale is argued to be corrupting, exploitative, or to express a form of disrespect. InMarkets without Limits, Jason Brennan and Peter Jaworski have recently argued to the contrary: For any good, as long as it is permissible to give it for free, then it is permissible to give it for money. Their thesis has led to a number of engaging objections, and I leverage recent work on the nature of feasibility within political philosophy to offer a new challenge.I argue that feasibility offers a constraint on which markets can be permissibly implemented. Though it may be possible to create a morally acceptable version of an otherwise repugnant market, some of these markets may be infeasible, and so we are not permitted to implement them. After laying out this challenge, I consider several replies. They concern the relevance of feasibility, and whether any markets really are infeasible. This provides an opportunity to explore the dangers of pursuing the infeasible and with markets generally. I conclude by considering what might lead us to pursue these markets despite their infeasibility, or how knowledge of infeasibility may prove useful regardless.