We study sequential bargaining between a proposer and a veto player. Both have single‐peaked preferences, but the proposer is uncertain about the veto player's ideal point. The proposer cannot commit to future proposals. When players are patient, there can be equilibria with Coasian dynamics: the veto player's private information can largely nullify proposer's bargaining power. Our main result, however, is that under some conditions there also are equilibria in which the proposer obtains the high payoff that he would with commitment power. The driving force is that the veto player's single‐peaked preferences give the proposer an option to “leapfrog,” that is, to secure agreement from only low‐surplus types early on to credibly extract surplus from high types later. Methodologically, we exploit the connection between sequential bargaining and static mechanism design.