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 ≤ 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)

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