Will a growing population lead to depletion of natural resources and eventually economic collapse, as predicted by Malthus, or rather to innovations in the agricultural sector improving agricultural potential of land, as hypothesized by Boserup? This centuries-old puzzle is as relevant as ever in some densely populated regions of Sub-Saharan Africa where population growth is still alarmingly high and shows no sign of slowing down, leading to enormous pressure on land. In this paper, we quantify the relationship between population pressure and land intensification in Burundi, one of the most densely populated regions in Africa. Using data from a nationally representative agricultural survey (n=2050), we find evidence of both Malthusian and Boserupian processes. In line with Boserup’s theory, the use of fertilizer and labour, yields and food production initially increases with population pressure, but decreases again when population densities exceed a critical threshold, supporting Malthus’ prediction. These limits to intensification confirm findings from previous studies on densely populated regions in Sub-Saharan Africa.