Using the ETFSI ( extended Thomas-Fermi plus Strutinsky integral ) method , we have calculated the fission barriers of nearly 2000 exotic nuclei , including all the neutron-rich nuclei up to A = 318 that are expected to be relevant to the r-process , and all superheavy nuclei in the vicinity of N = 184 , with Z \leq 120 . Our calculations were performed with the Skyrme force SkSC4 , which was determined in the ETFSI-1 mass fit . For proton-deficient nuclei in the region of N = 184 we find the barriers to be much higher than previously believed , which suggests that the r-process path might continue to mass numbers well beyond 300 . For the superheavy nuclei we typically find barrier heights of 6–7 MeV . PACS : 24.75.+i ; 95.30.Cq ^ { * } Supported in part by FNRS ( Belgium ) and NSERC ( Canada )