We consider axiomatic models of bargaining defined over a domain of problems containing different numbers of agents, define a concept called restricted monotonicity with respect of changes in the number of agents, and show that a solution due to Lahiri (1988), which satisfies monotonicity with respect to the disagreement point, meets the aforementioned requirement. Finally, we consider a class of solutions which are defined with respect to a reference point [concept due to Thomson (1981)] and show that this class satisfies our axiom of restricted monotonicity.