This paper deals with the status of heads in Head-Driven Phrase Structure Grammar (HPSG). Firstly, background assumptions are presented: the lexical representation of valence at the head and projection of head features. Secondly, I discuss criteria for determining the head of a phrase. I use nominal structures as an example, since the DP/NP debate is still undecided across frameworks, and exploring the arguments from an HPSG perspective may be interesting for readers. Zwicky’s (1985) criteria are discussed, and I show that most of them do not decide the issue for German nominal structures, but assignment of semantic roles by relational nouns and selectional relations in idioms (Osborne & Groß 2012, Bruening 2020) support NP structures. I di...