The standard problem of adjudicating conflicting claims describes a situation in which a given amount of a divisible good has to be allocated among agents who hold claims against it exceeding the available amount. This paper considers more general rationing problems in which, in addition to claims, there exist baselines (to be interpreted as objective entitlements, ideal targets, or past consumption) that might play an important role in the allocation process. The model we present is able to accommodate real-life rationing situations, ranging from resource allocation in the public health care sector to international protocols for the reduction of greenhouse emissions, or water distribution
in drought periods. We define a family of allocation methods for such general rationing problems - called baseline rationing rules - and provide an axiomatic characterization for it. Any baseline rationing rule within the family is associated with a standard rule and we show that if the latter obeys some properties reflecting principles of impartiality, priority and solidarity, the former obeys them too.