This paper focuses on the role of the efficiency gap in determining whether or not domestic firms benefit from productivity spillovers from FDI. We use establishment level data for the period 1980-1992 for the UK. Given that there is substantial heterogeneity of productivity across sectors we focus on two manufacturing sectors in detail, namely, electronics and engineering. We allow for different effects of FDI on establishments located at different quantiles of the productivity distribution by using conditional quantile regression. Overall, while there is some heterogeneity in results across sectors and quantiles, our findings clearly suggest that the efficiency gap matters for productivity spillover benefits. We find evidence for a u-shaped relationship between productivity growth and FDI interacted with the efficiency gap. We also analyse in some detail the impact of changes in relative efficiency on establishments' ability to benefit from spillovers.