We use a copula approach to investigate the effect of uncertainty on crude-oil returns. Using copulas to construct multivariate distributions of time-series data permit the calculation of the dependence structure between the series independently of the marginal distributions. Further, we implement the copula estimation using a rolling window method to allow for a time-varying effect of equity and economic policy uncertainty on oil returns. The results show that higher uncertainty, as measured by equity and economic policy uncertainty indices, significantly increase crude-oil returns only during certain periods of time. That is, we find a positive dependence prior to the financial crisis and Great Recession. Interestingly, estimation of the copula over the entire sample period leads to a negative dependence between the equity and economic policy indices and the crude-oil return.