Strategic uncertainty is the ambiguity that players face in games against other strategic opponents. Research shows that attitudes toward strategic uncertainty are source dependent, i.e., a player may express an aversion to or preference for strategic uncertainty depending on the game. One game may also be more or less uncertain than another. Which characteristics of a game determine the perceived level of and preference for strategic uncertainty? We propose to experimentally investigate the role of iterative reasoning (iterative best response or iterative application of dominance) on strategic uncertainty. By varying the parameters of a beauty contest game, we can turn iterative reasoning on and off and vary the number of reasoning steps required to reach the Nash equilibrium. We propose to measure strategic uncertainty attitudes using the belief hedges approach of Baillon et al. (2021). With further treatments, we can study when iterative reasoning makes a game more or less uncertain.