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Many game-theoretic models of crisis bargaining find that under incomplete information, an initial offer is either accepted, or war occurs. However, this finding is odd in two ways: (a) empirically, there are many cases of an agreement being peacefully reached after a number of offers and counteroffers and (b) theoretically, it is not clear why a state would ever leave the bargaining table and opt for inefficient war. We analyze a model in which, as long as the dissatisfied state is not too impatient, equilibria exist in which an agreement is peacefully reached through the offer–counteroffer process. Our results suggest that private information only leads to war in conjunction with other factors that are correlated with impatience, such as domestic political vulnerability, exogenous obstacles to the ability to make counteroffers rapidly, and bargaining tactics that create incentives to strike quickly or that lock the actors into war.