Multiplicity of sequential equilibria is a common problem in bargaining models with incomplete information in which the informed player makes an offer. Most of these equilibria are supported by optimistic conjectures by the uninformed player. This paper reexamines the bargaining model in Rubinstein (1953). Monotonicity restrictions are placed on off-the-equilibrium-path beliefs to exclude equilibria supported by optimistic conjectures. Sequential equilibria that survive these restrictions are characterized.