The study of the link between debt and growth has been full of debates, both in theory and empirics. However, there is a growing consensus that the relationship is sensitive to the level of debt. Our paper tries to address the question of non linearity in the long term relationship between public debt and economic growth. Specifically, we set out to test if there exists an established ‘laffer curve’ type relationship, where debt contributes to economic growth up to a certain point (maximal threshold) and then starts to have a negative effect on growth afterwards. To carry out our tests, we have used a methodology that delivers a superior test of bell shapes, in addition to the traditional test based on a regression with a quadratic specification. The results show evidence of a bell-shaped relationship between economic growth and total public debt in a panel of low income Sub-Saharan African economies. This supports the hypothesis that debt has some positive contribution to economic growth in low-income countries, albeit up to a point. If debt goes on increasing beyond the level where it would be sustainable, it may start to be a drag on economic growth.