Now that my gifts have wended their way across the oceans and been opened, I can show them off here.
First, a lot of split rings and some chains in variegated red and green quilting thread with a backing of white sewing cotton. This one also has red and green seed beads at most of the picot joins. The central band of split rings is not attached to any other part of the tatting -- it's just floating there. The pattern was accidentally adapted from another of my ornament patterns. Hey, I made it up, I ought to know how it goes. Nope. This worked out really well anyway -- once that central band was added.
The tatting is pinned to the green satin ornament with gold pins passed through a red seed bead. I used to lace the tatting onto the ornaments with gold or silver thread, but had a hard time getting them straight. Pinning works better for me.