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While Nash equilibria are guaranteed to exist, they may exhibit dense support, making them difficult to understand and execute in some applications. In this paper, we study \(k\)-sparse commitments in games where one player is restricted to mixed strategies with support size at most \(k\). Finding \(k\)-sparse commitments is known to be computationally hard. We start by showing several structural properties of \(k\)-sparse solutions, including that the optimal support may vary dramatically as \(k\) increases. These results suggest that naive greedy or double-oracle-based approaches are unlikely to yield practical algorithms. We then develop a simple approach based on mixed integer linear programs (MILPs) for zero-sum games, general-sum Stackelberg games, and various forms of structured sparsity. We also propose practical algorithms for cases where one or both players have large (i.e., practically innumerable) action sets, utilizing a combination of MILPs and incremental strategy generation. We evaluate our methods on synthetic and real-world scenarios based on security applications. In both settings, we observe that even for small support sizes, we can obtain more than \(90\%\) of the true Nash value while maintaining a reasonable runtime, demonstrating the significance of our formulation and algorithms.