Problem with multiple paragraphs floating around large image

Ran into a situation again where my p tags do not wrap around a large floated left (or right) image.  I've seen a few questions asked online, but no satisfactory answers.  Planting the image within the first p tag or keeping it out doesn't help; specifying clear:none on the image, on the paragraphs doesn't help.  Specifying display:inline helps a bit too much; the paragraphs stops being paragraphs.  Enough with css solutions.

Using a br tag(s) (single or multiple) looks different under various browsers.

Oddly, what works is defining a class of divs that act like the p tags.  These wrap fine.  Weird.