In this article we define and characterize a class of asymmetric leximin solutions, that contains both the symmetric leximin solution of Imai and the two-person asymmetric Kalai-Smorodinsky solution of Dubra  as special cases. Solutions in this class combine three attractive features: they are defined on the entire domain of convex n-person bargaining problems, they generally yield Pareto efficient solution outcomes, and asymmetries among bargainers are captured by a single parameter vector. The characterization is based on a strengthening of Dubra’s  property Restricted Independence of Irrelevant Alternatives (RIIA). RIIA imposes Nash’s IIA (Nash ), under the added condition that the contraction of the feasible set preserves the mutual proportions of players’ utopia values. Our axiom, entitled RIIA for Independent Players (RIP), says RIIA holds for a group of players, given that the contraction of the feasible set does not affect players outside that group.