The identification of a compound as endocentric or exocentric depends on the notion of head: if a compound has a head (or two) it is called endocentric, if it has no head is called exocentric. Exocentricity, however, has been usually assumed as a unitary notion, exactly because the notion of head has been generally interpreted as a unitary notion. In this paper we will first provide typologically based data on the dimension and on the limits of exocentricity, then we will argue that the notion of head can be split in three different subparts: categorial head, semantic head and morphological head. Correspondently, the notion of exocentricity can be split in categorial exocentricity, semantic exocentricity and morphological exocentricity. Our approach, based on features of the constituents and not on constituents as a whole, will hopefully provide a new analysis of exo- centricity in compounding.