[dspillett]

I've seen this done with one of the existing tags and appropriate nesting. <h1> for masthead, <h2> for major subdivisions in a huge page (essentially sub-mastheads), then <h3> for everything else with styling (and nesting in ToCs and such) being dictated either by how nested they are in <section> tags (or <div>s with an appropriate class). H3 here becomes a neutral header, and h4+ are just not used (nor is H2 in short/medium pages).

[Popeyes]

How does that help with a document structure if everything on the h3 level is the same?

I wish there was a neutral <h> element that could then be specified at an arbitrary <h~n~> sometimes I have documents that have headings 8 levels deep.