We report experimental results and test cooperative models of unstructured bargaining by checking the empirical relevance of the underlying axioms. Our data support strong efficiency, symmetry, independence of irrelevant alternatives and monotonicity, and reject scale invariance. Individual rationality and midpoint domination are violated by a significant fraction of agreements that implement equal division in highly unequal circumstances. Two well-known bargaining solutions that satisfy the confirmed properties explain the observed agreements reasonably well. The most frequent agreements in our sample are the ones suggested by the equal-division solution. In terms of the average Euclidean distance, the theoretical solution that best explains the data is the deal-me-out solution (Sutton, 1986; Binmore et al., 1989, 1991). Popular solutions that satisfy scale invariance, individual rationality, and midpoint domination, as the well-known Nash or Kalai-Smorodinsky bargaining solutions, perform poorly in the laboratory.