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After a lot of experimenting, I found a method of nalbinding that works for me. The stitch is known as the Mammen Stitch, as it was found in a grave in Mammen, Denmark. It's very pleasing to the eye, and well worth the effort to try to reproduce.
(This information is available as a one-page .PDF handout sponsored by furcadia.com http://lamp.youlanda.com/nalbinding/nalbinding.pdf )
1. Thread a large needle.
2. Make a slipknot. Hold it gently pinched.
3. Lightly wrap your finger.
Put the needle through the first loop and below the loop on your finger.
4. Slip your finger out of the loop. Pinch it to hold it still and keep it the same size.
5. Form a fresh loop around your finger as you go through the next steps:
Go through the last two loops you're pinching, needle pointing towards yourself.
Go through the last loop, needle pointing away from yourself.
6. Release the loop around your finger.
7. Repeat as in Step 5: Go towards yourself through the last two loops; go away from yourself through the last loop; form a new loop arond your finger as you do this.
8. Go through previous loops to add more rows.
The book by Sigrid Briansdotter (Nalbinding Made Easy) teaches a thumb method. She's done huge amounts of research and if anybody would know what hand position was used, I think it probably would be her.
The Mammen Stitch has 'parity'. One side of the edge is concave and the other side slightly convex. By alternating the thumb and finger methods, you can go back and forth (analogous to 'knit' vs. 'purl'). If you create something in a spiral or tubular path, the project will stay smooth naturally.