Defeat between arguments is established by a combination of two basic elements: a conflict or defeat relation, and a preference relation on the arguments involved in this conflict. We present a new abstract framework for argumentation where two kinds of defeat are present, depending on the outcome of the preference relation: an argument may be a proper defeater or a blocking defeater of another argument. An operator is used to characterize the set of accepted arguments. This operator also provides a method for identifying controversial situations.