flat round peyote stitch?

I've been working on making a little round peyote box, and so far I've
been pleased with the results..except when it comes to making the
bottom and lid. I looked up a tutorial for even count flat round
peyote stitch, but no matter how carefully I follow it, I end up with
a round piece of peyote that's ruffled rather than flat. I've tried
relaxing the thread tension, but that just gave me a very floppy
ruffly piece. I tightened the thread tension and got a rigid ruffled
piece. Has anyone followed these directions with success?

http://rogue.northwest.com/~ahawley/flatround.htm

If anyone knows of some better instructions, please point me in that
direction, cause otherwise I'm going to have bottomless, topless
boxes.

-Amber.