In many bargaining situations a third party is authorized to impose a backstop position on the bargainers. Prominent examples include governments who use collaborative policymaking between stakeholders to set public policy, but also compulsory arbitration in labour negotiations. Axiomatic models of cooperative bargaining, such as the Nash bargain, presume that the status quo allocation will have no effect on the outcome parties reach if it differs from the backstop set by the third party. In contrast, experimental findings have suggested that both equality of outcomes and entitlement (where the status quo establishes a focal point) may affect the agreements bargainers reach, at least under full information. This paper extends the investigation of the effect of equality and entitlement on cooperative bargaining to the case where parties have private, unverifiable information concerning the value of outcomes. We use a two-party, two-attribute experimental design in which subjects take part in unstructured, face-to-face bargaining to jointly select from among approximately 200 potential outcomes. We find that, relative to full information, parties who bargain under private information are almost as likely to reach agreements as those under full information, and that these agreements are still approximately Pareto efficient. Further, the effect of the status quo (rather than backstop) allocation seems amplified under private information, while the effect of equality is dampened, but not eliminated.