Teepee help?

[http://users.livejournal.com/little_e_/]

I made a teepee for my son (he's almost 2). It consists of 5 wooden dowels, a thick shoelace to tie them together, and an old skirt with a slit up the side draped over it. He loves it, but as you might expect, constantly bumping into the poles (and standing up in the teepee to play peekaboo) causes them to shift--the biggest problem is that the poles contract, making the teepee progressively taller and narrower, until it falls over. It's fairly easy to right the teepee, but I'd rather he be able to play in it for more than 5 minutes at a time!

So, does anyone have any nifty solutions to my engineering problem? I was thinking of drilling holes in the tops of the dowels and in an embroidery hoop, and then screwing the hoop to the inside of the upper circle of dowels, but since the dowels are conical and the hoop cylindrical, this strikes me as very tricky (not to mention that the dowels are rather thin for this.)