This paper presents issues related to H tone spreading in Tsonga, a Bantu language spoken in South Africa and Mozambique. H tone spreading is blocked when a depressor consonant (voiced stops, breathy voice, and aspirates) is present. On the other hand, downstep occurs when H tone spreads toward another H tone. The H tone spreading and its results are analyzed within Optimality Theory. First, the depressor effect is analyzed with two markedness constraints; one requires tone on depressors, and the other one bans high tone on depressors. Crucially, no faithfulness constraint preserves underlying tone on consonants, so that consonants will not be contrastive in tone. This ensures that depressors do not appear with a H tone in the output. Second, downstep in Tsonga is argued to result from adjacent H tones in the output following Bickmore (2000).