The paper investigates a certain class of solutions to the bargaining problem with a varying set of agents belonging to a finite universe of agents. The class is defined by four conditions: symmetry, independence of irrelevant alternatives, continuity and monotonicity. Thus, no optimality conditions are involved. The main result is that any solution satisfying these conditions equals (except perhaps for a two-agent set) a socalled truncated egalitarian solution. This notion is introduced in the paper, ''truncation'' referring to the agent set involved. Such solutions are not in general optimal.