I think I just have to accept that the Nokia 1020 on default settings will drain the battery in 8 hours or so. I found this article, so I guess it is not just a Nokia issue.
I have tried changing the settings as described, and it does seem to have reduced the drain a bit. I will try it out tomorrow and see what happens.
When I contacted Nokia support, they told me that it was possible that out of the box settings would only provide 8 hours…..