Abstract: Neither Chun’s equal-loss nor Chun and Peter’s lexicographic equal-loss solutions for bargaining problems are individually rational. Chun and Peters proposed a modification of the lexicographic equal-loss solution guaranteeing individual rationality (without characterization). In this paper, we provide an axiomatic characterization of the aforementioned solution. Then, we propose and axiomatically characterize a new solution concept, which modifies Chun’s equal-loss solution in a way that ensures individual rationality. It turns out that its lexicographic extension coincides with Chun and Peter’s proposal.