This paper begins by presenting and strengthening the labial-velar hypothesis with a novel interpretation of the allophonic distributions of labials and velars in Lusoga (Hyman 2017). The labial-velar hypothesis is an Element Theory proposal that labial (Lab) and dorsal (Dors) consonants are marked by same ‘dark’ place feature |U| (akin to Jakobson & Halle’s (1956) grave). According to this hypothesis, the only difference between Lab and Dors members of any class (say stops) is that Lab is the headed manifestation of |U|, while Dors is the headless version of the same element (Backley & Nasukawa 2009). This, hypothesis however, leads to the strange statement that labial-velar segments such as the labial-velar ‘double’-stop (KP), which would appear to be headless and headed at the same time. What follows is an exploration of the term ‘headedness’ in phonology. Building on the positives of previous approaches, and pairing back the assumptions to the first principles of combination (Merge), I come up with a novel theory of headedness and segment-internal structure: Bare Element Geometry (BEG). The labial-velar hypothesis in light of BEG will then be applied to KP. In order to obtain the right representation for labial-velar ‘double’-stops (KP), it is necessary to precisely understand KP’s distribution and behaviour. Especially because I will reveal some previously unappreciated facts about these segments. In opposition to the classical literature (and all previous accounts known to me), I will conclude that KP is composed of two ordered root nodes, each with a separate place feature. This is based on a detailed typological study and phonological interpretation of attested and unattested nasal + KP assimilation patterns, as well as a novel interpretation of some obscure nasalization facts of KP in Guere (Western Kru). This conclusion that KP has two ordered root nodes is what allows BEG’s model of headedness to interpret a feature as simultaneously headed and headless in different parts of a segment. Moreover, it correctly predicts Cahill (1999)’s empirical observation that KP is universally headed by Labial.