Harsanyi type structures, the device traditionally used to model players' beliefs in games, generate infinite hierarchies of beliefs. Can the standard framework nevertheless be used to model situations in which players potentially have a finite depth of reasoning? This paper extends the Harsanyi framework to allow for higher-order uncertainty about
players' depth of reasoning. The basic principle is that players with a finite depth of reasoning cannot distinguish states that differ only in players' beliefs at high orders. I apply the new framework to the electronic mail game of Rubinstein (1989). Coordination on the Pareto-efficient action is possible when there is higher-order uncertainty about
players' depth of reasoning, unlike in the standard case, provided that one player thinks it is sufficiently likely that the other player has a finite (though potentially very high) depth of reasoning. Finally, I construct a type space that allows for bounded reasoning that contains the universal type space (which generates all infinite belief hierarchies) as a subspace, showing that the present framework fully generalizes the Harsanyi formalism.