|Abstract:||McCarthy (2004) shows that OT-based theories of featural and tonal assimilation to date are inadequate for two reasons: (i) they fail to distinguish between candidates showing varying degrees of harmony; (ii) or, they achieve assimilation disingenously (i.e. via unattested repairs). In response, McCarthy (2004) proposes a theory of Headed Spans, whose success improves upon that of its OT predecessors, particularly insofar as it avoids the pathological predictions mentioned above. The goal of this article is to further examine Headed Spans by attempting to analyze several productive phenomena found in Bantu tonal systems. Accordingly, I propose some specific revisions and additions to Headed Spans that I argue are necessary to bring both tone displacement and a surprising case of unconditional binary spreading into submission.