The class of defeasible logics is only vaguely defined -- it is defined by a few exemplars and the general idea of efficient reasoning with defeasible rules. The recent definition of the defeasible logic $DL(\partial_{||})$ introduced new features to such logics, which have repercussions that we explore. In particular, we define a class of logics that accommodates the new logic while retaining the traditional properties of defeasible logics.