We examine strategic sophistication using eight two-person 3 × 3 one-shot games. To facilitate strategic thinking, we design a ‘structured’ environment where subjects first assign subjective values to the payoff pairs and state their beliefs about their counterparts’ probable strategies, before selecting their own strategies in light of those deliberations. Our results show that a majority of strategy choices are inconsistent with the equilibrium prediction, and that only just over half of strategy choices constitute best responses to subjects’ stated beliefs. Allowing for other-regarding considerations increases best responding significantly, but the increase is rather small. We further compare patterns of strategies with those made in an ‘unstructured’ environment in which subjects are not specifically directed to think strategically. Our data suggest that structuring the pre-decision deliberation process does not affect strategic sophistication.