Rubinstein's alternating-offers bargaining model is enriched by assuming that players' payoffs in disagreement periods are determined by a normal form game. It is shown that such a model can have multiple perfect equilibria, including inefficient ones, provided that players are sufficiently patient. Delay is possible even though there is perfect information and the players are fully rational. The length of delay depends only on the payoff structure of the disagreement game and not on the discount factor. Not all feasible and individually rational payoffs of the disagreement game can be supported as average disagreement payoffs. Indeed, some negotiation games have a unique perfect equilibrium with immediate agreement.