We present a theoretical framework for tone that builds on the Headed Spans theory of assimilation. We propose that spans have two important properties, which we term binarity and minimal overlap. Cilungu (Bantu, Zambia) exhibits a process of binary H tone spreading onto the following mora, and then onto the following syllable, unless an Obligatory Contour Principle (OCP) violation would result. We propose two binary constraints on spans to explain this pattern. Further, Cilungu binary spreading obtains regardless of the length of the sequence of H-toned tone-bearing units (TBUs) in the input, which creates arbitrarily long output sequences of H-toned TBUs. We show that the binarity analysis can nonetheless account for this generalisation if spans are permitted to minimally overlap. A welcome consequence of permitting minimal overlap is that the No Crossing Condition can be derived (for tone) from factorial typology: candidates with supraminimal overlap are harmonically bounded in our theory. Finally, the formal and typological pathologies of non-overlapping alternative analyses are discussed.