This paper studies the relationship between prosodic phrasing and prominence by addressing the questions of whether every prosodic phrase must have a head (a most prominent sub-constituent), and if so, how the head is marked. I study these questions by examining the intermediate phrase (iP) in English. If every iP must have a head, and this head must be marked by a pitch accent, then in an environment without any pitch accent, there should be no head/non-head distinction. And if there is no head, there should be no iP in this context either. I conducted a production study in English, and found durational evidence suggesting the presence of iP boundaries in an accent-less context. I also searched for durational evidence for iP-level prominence distinctions in this context, but here my results are mixed. One theoretical possibility that is compatible with my findings is that every phrase must have a head, but the head of an iP can be marked by something other than pitch accent, for example by phrasal stress.