Many papers have been documenting and analysing the asymmetry and the weakening of the oil price – macroeconomy relationship as off the early eighties. While there seems to be a consensus about the factors causing the asymmetry, namely adjustment costs which offset the benefits of low energy prices, the debate about the weakening of the relationship is not over yet. Moreover, the alternative oil price specifications which have been proposed by Mork (1989), Lee et al. (1995), and Hamilton (1996) to restore the stability of the relationship fail to Granger cause output or unemployment in post-1980 data. By using the concept of accelerations of the oil price, we show that the weakening of this relationship corresponds to the appearance of slow oil price increases, which have less impact on the economy. When filtering out these slow oil price variations from the sample, we manage to rehabilitate the causality running from the oil price to the macroeconomy and show that far from weakening, the oil price accelerations – GDP relationship has even been growing stronger since the early eighties.