Simultaneous bargaining over more issues by two bargainers is treated by taking sums of bargaining games and requiring bargaining solutions to satisfy certain (super-) additivity axioms. A (new) characterization of a family of so-called proportional solutions is given with the aid of three axioms: (partial) superadditivity, homogeneity, and weak Pareto optimality. Requiring, besides individual rationality and Pareto continuity, the axioms of restricted additivity, scale transformation invariance, and Pareto optimality, yields an alternative characterization of a family of solutions consisting of all nonsymmetric extensions of Nash's solution. Also these solutions exhibit a (limited) proportionality property. Further, the relation with the Super-Additive solution of Perles and Maschler is discussed, and also the link with Myerson's results on proportional and utilitarian solutions.