Strategic uncertainty is the uncertainty that players face with respect to the purposeful behavior of other players in an interactive decision situation. Our paper develops a new method for measuring strategic-uncertainty attitudes and distinguishing them from risk and ambiguity attitudes. We vary the source of uncertainty (whether strategic or not) across conditions in a ceteris paribus manner. We elicit certainty equivalents of participating in two strategic 2x2 games (a stag-hunt and a market-entry game) as well as certainty equivalents of related lotteries that yield the same possible payoffs with exogenously given probabilities (risk) and lotteries with unknown probabilities (ambiguity). We provide a structural model of uncertainty attitudes that allows us to measure a preference for or an aversion against the source of uncertainty, as well as optimism or pessimism regarding the desired outcome. We document systematic attitudes towards strategic uncertainty that vary across contexts. Under strategic complementarity [substitutability], the majority of participants tend to be pessimistic [optimistic] regarding the desired outcome. However, preferences for the source of uncertainty are distributed around zero.