Thanks, Hitch!
I suspected that it involved unzipping the epub first.
What I've been doing, since i work mostly in linux, is to first make a good epub for the rest of the world (and even Apple, if that's possible) using Sigil. When that's done, I edit a copy of that epub, again using Sigil, to make it suitable for kindlegen.
I.e. remove the CoverPage.xhtml, add the TOC.xhtml in the right place, other little tweaks as necessary and save.
I still have to unpack it and adjust content.opf to point the "cover" guide item to the cover image itself (instead of the .xhtml page I removed) and for completeness, change the title= of the text guide item to "Start Reading. Then rezip, and run it through kindlegen, and I'm done.
Almost takes longer to describe it than to do it.