  Dung's abstract framework for argumentation enables a study of the
interactions between arguments based solely on an ``attack'' binary relation on
the set of arguments. Various ways to solve conflicts between contradictory
pieces of information have been proposed in the context of argumentation,
nonmonotonic reasoning or logic programming, and can be captured by appropriate
semantics within Dung's framework. A common feature of these semantics is that
one can always maximize in some sense the set of acceptable arguments. We
propose in this paper to extend Dung's framework in order to allow for the
representation of what we call ``restricted'' arguments: these arguments should
only be used if absolutely necessary, that is, in order to support other
arguments that would otherwise be defeated. We modify Dung's preferred
semantics accordingly: a set of arguments becomes acceptable only if it
contains a minimum of restricted arguments, for a maximum of unrestricted
arguments.
