how to insert stuff above all content

I’m trying to write a plugin that prints some html inside the body, but above all of the reasonable content. I can’t find an action hook to do it!

I tried wp_head, but that’s in the header not the body.

I tried loop_start, but many themes seem to execute too many loops, so for instance with the thematic theme, my material appears twice in the header and once in the body. With certain widgets it can then appear again in the sidebar.

Any ideas?