We investigate the domain of comprehensive but not necessarily convex bargaining problems. Without convexity the Nash solution is not well defined. We propose a new solution, the Nash extension, that coincides with the Nash solution when S is convex. We characterize it by weak Pareto optimality, symmetry, scale invariance, continuity, and a new axiom, ethical monotonicity. Journal of Economic Literature Classification Numbers: 020, 022, 026.