I had the correct pun_bbcode extension, but I guess there was something I messed up somewhere else, since it works okay with a clean installation of the forum. I'll try starting from scratch again. Thanks for your answer.
The header bbcode enlarges the text. So I don't see the need for an extra tag.
My bad, I completely missed that tag in the BBCode help page...
I still could use a "small" tag, but it might not be too complicated to add by myself.