Thanks for the reply, happy_noodle_boy, but...
The linebreaks in the HTML is not the result of any specific formatting by TinyMCE or JCE (in fact a quick test revelaed that FCK and wysiwygpro behave in the same way). This may be a symptom of the HTML extraction from the converted textarea and does not appear to be browser specific.
On my site, FCK doesn't reformat the HTML, dunno about WysiwygPro. Strange..
Short of creating a special cleanup routine for JCE or TinyMCE, there does not seem to be any other way to "fix" this. Its not actually a bug, as it does not affect normal HTML creation (the rendered HTML and specifically the H2 block element are displayed correctly).
Isn't there, like a "don't cleanup" setting in 1. any setting somewhere or 2. special code, tag or else that tells that cleanup routine to ignore a certain line ? (This last one, 2, could be a nice FR, don't you think?
If you do not absolutely have to use a block element (ie: H2 etc) use a span instead and you will not have the problem.
I know, I know, but I have reasons to use the h2!