Bargaining under uncertainty is modeled by the assumption that there are several possible states of nature, each of which is identified with a bargaining problem. We characterize bargaining solutions which generate ex ante efficient combinations of outcomes under the assumption that the bargainers have minimax regret preferences. For the case of two bargainers a class of monotone utopia-path solutions is characterized by the efficiency criterion, but for more than two bargainers only dictatorial solutions are efficient. By incorporating scale covariance into the minimax regret preferences a possibility result is obtained for the general case. Journal of Economic Literature Classification Numbers: C78, D81, D71.