We examine the combined effects of oil dependence and the quality of institutions on economic growth. To do so, we introduce a new buffered thresholdpanel data model and apply it to 19 oil rent-dependent countries over the period 1996-2017. We show that the relationship between growth and oil dependence is not linear. More precisely, three categories of oil-dependentcountries are identified. Only countries with high-quality institutions are very stable. All the other countries have experienced a transition into a buffer zone and are potentially in a transition between two different regimes.When considering oil dependence as a threshold variable, it appears that the quality of institutions has a positive and significant effect on growth when dependence is either low or high. More interestingly, for countries with intermediate levels of oil-dependence, the quality of the institutions negatively impacts growth. Some of these countries have experienced something of an oil-dependence trap.