We collect experimental evidence on a modified version of the standard ultimatum game in which the responder states an acceptance threshold below which the offer is rejected and both players, proposer and responder, are allowed several attempts to reach an agreement by conceding. Proposers concede by increasing offers and responders concede by decreasing acceptance thresholds. Treatments differ in whether a further attempt requires that at least one party should have conceded. A further condition varies the number of possible negotiating attempts, namely, 3 versus 5. Behavior in the lab diverges significantly from the theoretical solution in which the proposer is expected to get nearly the whole pie in each treatment. Proposers (responders) initially offer less (ask more) and concede more across negotiation attempts in the treatment in which concessions are required. Moreover, compulsory concessions weaken the bargaining position of the proposer, who eventually gets significantly less. Finally, although concessions significantly improve the likelihood of an agreement compared to standard ultimatum game experiments, the longer negotiation horizon (five attempts instead of three) delays the agreement without enhancing it, even when no concessions are needed.