I followed the tutorial, except I used old tights and nylons instead of fabric and wire twist ties instead of string to wrap them up. I also saw that Family Fun recently published their own version of this craft, and they have you just secure the piece of silk to the egg with rubber bands. I guess the only advantage to using an outer layer is you can use a smaller piece of silk.
I have enough silk left over from the ties we used last year to do at least a couple more eggs each, but since so much of the fun is in the mystery of how each print will come out, I'd much rather do it again with different ties. I think I need to arrange some sort of old tie swap. Anybody interested?