I consider a model of reputational bargaining in which the stubborn type can choose their initial demand. There are two types of players: rational and stubborn. The game has two stages: a demand stage and a concession stage. Types can pool or separate in equilibrium for any fixed probability of facing a stubborn type. When the probability of facing a stubborn type is small, any feasible payoff can be achieved in equilibrium for either type. When the probability is large, there is either immediate agreement or long delays.