Improving knowledge about African historical demography is essential to addressing current population trends and achieving deeper understanding of social, economic, and political change in the past and present. I use census and parish register data from Tanganyika to address the origins of twentieth-century population growth, to describe how major changes in fertility and child mortality began in the 1940s, and to emphasise the significance of the large rise in fertility between the 1940s and 1970s. Through this work and my wider survey of parish registers in Malawi, Uganda, Tanzania, and Zambia, I consider the relationships between power, evidence, and meaning in these data sources. Alongside the macro gaps in Africa's population history are significant microsilences — lacunae in the sources and data which reflect the hegemonic structures within which they were produced. I suggest a moral demography approach to their analysis, borrowing from the reflexive and dialectic method found in studies of moral economy.