We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players in return for some payment among players. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium of this game which is essentially unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and nondeterministically. The better informed player obtains a rent.