The paper describes the University of Cape Town’s submission to the constrained track of the WMT22 Shared Task: Large-Scale Machine Translation Evaluation for African Languages. Our system is a single multilingual translation model that translates between English and 8 South / South East African Languages, as well as between specific pairs of the African languages. We used several techniques suited for low-resource machine translation (MT), including overlap BPE, back-translation, synthetic training data generation, and adding more translation directions during training. Our results show the value of these techniques, especially for directions where very little or no bilingual training data is available.