The seminal cobweb model by Brock and Hommes reveals that fixed-point dynamics may turn into increasingly complex dynamics, as firms switch more quickly between competing expectation rules. While policy makers may be able to manage such rational routes to randomness by imposing a proportional profit tax, the stability-ensuring tax rate may cause a very high tax burden for firms. Using a mix of analytical and numerical tools, we show that a rather small profit-dependent lump-sum tax may even be sufficient to take away the competitive edge of cheap destabilizing expectation rules, thereby contributing to market stability.