ePub->fb2 (what am I doing wrong?)

Hello. I'm trying to convert some of my ePubs into FB2 (in batch, but I don't think it's important - butch or no butch). Here's the problem:
The resulting file FB2 is readable, it includes all images, so far so good, but... It's completely unstructured, that is, no parts, chapters, and any other titles-subtitles tags. So I can't go to, let's say, Chapter 4, and unable to see the structure of the book at all.
On the other hand, ePub is a compressed collection of HTMLs, so it should be easy enough for Calibre to replace HTML headers wih FB2 tags. How should I force the program do what I need and what would be a more or less nice and usable FB2 file?

(I'm sure there's some answer to this.)

Thank you in advance.