An extension of the standard rationing model is introduced. Agents are not only identified by their respective claims to some amount of a scarce resource, but also by some exogenous ex-ante conditions (initial stock of resource or net worth of agents, for instance), other than claims. Within this framework,we define a generalization of the constrained equal awards rule and provide two different characterizations of this generalized rule. Finally, we use the corresponding dual properties to characterize a generalization of the constrained equal losses rule.