Abstract: The problem of distributing a given amount of a divisible good among a set of agents which may have individual entitlements is considered here. A solution to this problem, called the Rights–Egalitarian Solution is proposed. This allocation rule divides equally among the agents the difference between the aggregate entitlements and the amount of the good available. A relevant feature of the analysis developed is that no sign restriction is established on the parameters of the model (that is, the aggregate entitlement may exceed or fall short of the amount of the good, agents’ rights may be positive or negative, the allocation may involve a redistribution of agents’ holdings, etc.). This paper provides several characterizations of this rule and analyzes its game theoretical support.