We extend the Ståhl–Rubinstein alternating-offer bargaining procedure to allow players to simultaneously and visibly commit to some share of the pie prior to, and for the duration of, each bargaining round. If commitment costs are small but increasing in the committed share, then the unique subgame perfect equilibrium outcome exhibits a second mover advantage. In particular, as the horizon approaches infinity, and commitment costs approach zero, the unique bargaining outcome corresponds to the reversed Rubinstein outcome (δ/(1+δ),1/(1+δ)), where δ is the common discount factor. •We extend the alternating-offer bargaining model.•At the start of each bargaining round, each party may commit to a share of the pie.•When commitment costs are small but increasing, there is a second mover advantage.•This reverses the sharing of Rubinstein (1982).