This, the second lecture, shows how to build a syntactic system that separates the building of structures from their labelling via the elimination of all heads from the syntax, except semantically contentful roots (an extension of the system presented in Adger 2013). No heads means no head movement, and I briefly show how word building and positioning can be captured in such a system via what Adger and Svenonius (2010) called second order interface features (essentially following the insights, if not the implementation, of Brody's 2000 Mirror Theory). But this lecture is mainly about Roll-Up derivations, which also do not feed semantics. The theory I present not only rules out head movement, it also makes Roll-Up derivations impossible, though it allows a kind of base generated alternative. I present some evidence from asymmetries between binding and linear order in prepositional phrases that suggest the such a theory is empirically, as well as theoretically, preferable to one employing Roll-Up.