This paper investigates the ability of individuals to make complex chains of reasoning, similar to those underlying the logic of iterated deletion of dominated strategies. Controlling for other-regarding preferences and beliefs about the rationality of others, we show, in the laboratory, that the ability of individuals to perform complex chains of iterative reasoning is better than previously thought. We conclude this from comparing our results with those from studies that use the same game without controlling for confounding factors. Subjects were able to perform about two to three iterations of reasoning on average as measured by our version of the Red-Hat Puzzle.