Reprocessing some kinds of nuclear waste actually reduces long-term radiation levels. TRUEX, from Argonne National Laboratory, can remove (and then burn up) transuranic alpha emitters, and basically you end up with short-lived high activity isotopes (safely stored above ground for decades in fuel ponds on-site) and long-lived low-activity isotopes (fairly similar to the natural ores, and could be stored underground long-term, or in subduction zones in the mantle). The problem is that doing this has a proliferation risk, but I have zero fear of the Japanese developing a nuclear weapon, and as far as the US, UK, FR, CN, RU doing so, well, that ship sailed in the middle of last century.
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Reprocessing some kinds of nuclear waste actually reduces long-term radiation levels. TRUEX, from Argonne National Laboratory, can remove (and then burn up) transuranic alpha emitters, and basically you end up with short-lived high activity isotopes (safely stored above ground for decades in fuel ponds on-site) and long-lived low-activity isotopes (fairly similar to the natural ores, and could be stored underground long-term, or in subduction zones in the mantle). The problem is that doing this has a proliferation risk, but I have zero fear of the Japanese developing a nuclear weapon, and as far as the US, UK, FR, CN, RU doing so, well, that ship sailed in the middle of last century.