This paper examines the relationship between hydrocarbon and non-hydrocarbon revenues using a probabilistic panel model with data covering 30 resource-rich countries over 1992-2012. It also discusses policy implications for Uganda, a country with recently discovered oil reserves. The findings show that although an increase in hydrocarbon revenues is likely to crowd out non-resource revenues, improved institutional quality could dampen or reverse this effect. In general, regulatory quality, rule of law, government effectiveness, and political stability are critically important governance indicators. In light of Uganda's forthcoming exploitation of its oil, the odds of avoiding the crowding out of non-resource revenues are high with a substantial improvement of institutional quality in terms of political stability, regulatory quality, and government effectiveness. Currently, these indicators stand very low for Uganda as compared with Botswana