Coalitional aspects of bargaining are investigated. Binary trees describe coalition structures; at a vertex the payoffs are distributed linearly according to parameters for the two sets. The parameter for a player-set is assumed to be the sum of the parameters in that set. These values are the subject of bargaining. The criteria for the results of bargaining are formulated, thus determining a bargaining point(s) in the space R of the parameters. R can be divided into regions in which a particular tree is maximal. In completely essential 3-player games these regions are simply connected; the bargaining point is where these regions meet. The solutions for 4- and n-player games present immense problems. Our solutions are compared with other solution concepts. We show that in the 3-player game our solution is monotonic but not completely coalitionally monotonic.